13_FMML_Course_Probability_Primer.ipynb

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      "source": [
        "# Statistics and Probability: Fundamentals"
      ]
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      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from matplotlib import pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "import plotly.graph_objects as pg\n",
        "import plotly.express as px"
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      "source": [
        "# What is Probability?"
      ]
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        "## Definitions\n",
        "\n",
        "In nature as in Compute Science, one of several events can be predicted to occur, but we do not know exactly which of them will occur. The supposition is that they will occur with different frequencies, and we know those frequency. So each time we run the experiment, we call is a **sample**.\n",
        "\n",
        "The thing that we are computing the probability of is typically a boolean condition.\n",
        "* Whether or not the sample belongs to a set: Does a integer sampled randomly belong to the set of natural numbers?\n",
        "* Any set of boolean conditions on that set: Is an integer samples randomly prime, and it's either greater than 100 or less than 50.\n",
        "* By membership in a continuous set: Is the speed of the car in the range 60 to 80.8 km per hour.\n",
        "\n",
        "Given this boolean formulation, we can construct a set of elements which we are computing the probability of. We will call these favorable samples.\n",
        "\n",
        "$$P = \\frac{\\text{number of favorable samples}}{\\text{number of samples}}$$\n",
        "\n",
        "For now assume that all samples in our set of all possibilities (i.e. sample space) are equally likely. This need not be true, the samples can themselves be chosen from some probability distribution, a proposition which we will encounter when we study conditional probability."
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        "def toss_coin(number_of_tosses=100):\n",
        "    return pd.Series(np.random.choice(['Heads', 'Tails'], number_of_tosses))\n",
        "\n",
        "def throw_dice(number_of_tosses=100):\n",
        "    return pd.Series(np.random.randint(1, 6+1, number_of_tosses))"
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        "results = toss_coin()\n",
        "print(results.value_counts())\n",
        "fig = pg.Figure([pg.Bar(x=results.value_counts().keys(), \n",
        "                        y=results.value_counts().values)])\n",
        "fig.show()"
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          "text": [
            "Heads    54\n",
            "Tails    46\n",
            "dtype: int64\n"
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        "## Derived Probability Distributions\n",
        "\n",
        "Given the simple fact that each toss will be heads or tails (also called a bernoulli distribution) we can come up with a derived question, that given 20 coin tosses, what is the probability that 7 of them are heads.\n",
        "\n",
        "You can see the probability distribution below, it's called a Binomial distribution and looks like a Bell. This will always happen whenever you have a bunch of independently sampled variables. (Independent and Identical, see Central Limit Theorem)"
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      "source": [
        "results = pd.Series([np.sum(toss_coin(20) == 'Heads') for _ in range(1000)])\n",
        "fig = pg.Figure([pg.Bar(x=results.value_counts().keys(), \n",
        "                        y=results.value_counts().values)])\n",
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LTpBI0ayWqL7"
      },
      "source": [
        "Let's try to see if we toss the coin 500 times, then what happens. Looks similar, and more like a bell than before."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "4YvjeQGwqUj1",
        "outputId": "5c840ae0-eaf4-471b-d091-4c6217a5d1cc"
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      "source": [
        "results = pd.Series([np.sum(toss_coin(500) == 'Heads') for _ in range(5000)])\n",
        "fig = pg.Figure([pg.Bar(x=results.value_counts().keys(), \n",
        "                        y=results.value_counts().values)])\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
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      "source": [
        "## How much to Sample\n",
        "\n",
        "It's hard to estimate the probability of real world events experimentally. Like what is the probability of rolling a dice and getting a 2. Well, it's 1/6, easy to see theoretically. Often it won't be, in which case we need to see from experiments what the answer is.\n",
        "\n",
        "We have the 1/6 theoretical result as a Red line. The probability of getting each number from 1 to 6 is shown, but the different colors represent the different number of experiments it was sampled from. Blue was estimated using 10 experiments, Red using 100, Green with a 1000, Purple with 10000, and Orange with 100000. You can see that as we get more samples, the correctness and the reliability of that correctness increases.\n",
        "\n",
        "You can also see, that if we took 100 samples, and we have a value far away from 1/6, taking more samples will take us back to 1/6 in time. This phenomenon is called **Regression to the Mean** and you can hear more about it in the following Veritasium videos."
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        "results = {shots: throw_dice(shots) for shots in [10, 100, 1000, 10000, 1000000]}\n",
        "fig = pg.Figure([pg.Bar(x=result.value_counts().keys(), \n",
        "                        y=result.value_counts().values / shots,) \n",
        "                    for shots, result in results.items()])\n",
        "fig.add_shape(type='line', x0=0.5, y0=1/6, x1=6.5, y1=1/6, line=dict(color='Red',))\n",
        "fig.show()"
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    {
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      "source": [
        "## Traps of Statistics in the Real world\n",
        "\n",
        "Vertiasium and 3Blue1Brown are some of the best instructors in taking phenomena in the real world and taking them apart in the language of mathematics, analyzing how good and correct are the solutions we pose to them. Following couple of videos are excellent demonstrators of how we apply probability in the real world, and how the entire world might often misapply it, or atleast misinterpret or partially interpret what the math is saying. Do take a look.\n",
        "\n",
        "* Veritasium: Is most published research wrong? https://youtu.be/42QuXLucH3Q\n",
        "* Veritasium: How we're fooled by statistics https://youtu.be/1tSqSMOyNFE"
      ]
    },
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      "cell_type": "markdown",
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        "## Try to solve for these\n",
        "\n",
        "1. If you have a shuffled deck of 52 cards, there are 4 aces, 4 kings, 4 queeens, 4 jacks, and 4 of each numbered card from 2 to 10. What is the probability that if you draw a card at random it will be a numbered card.\n",
        "\n",
        "2. In the same setup as above, you take on card out and look at it, put it back into the deck and shuffle it. Now you pull another card output. What is the probability that both the cards you pulled out are numbered cards.\n",
        "\n",
        "3. Same Problem as above, but now when you pull out one card, you throw it out and do not put it back into the deck. Find the probability now that they are both numbered cards that you drew.\n",
        "\n",
        "4. Now the deck of card is not shuffled. All the cards are in sorted order, first all the cards from Ace to King of Spades, then Hearts, then Diamonds and then Clubs. You are asked to cut the deck (break it into 2 parts, i.e. pick some cards from the top) at a random location. What is the probability that the bottom card of your cut is an numbered cards card."
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        "## Fundamentals of Probability\n",
        "\n",
        "For your reference, the rules of probability are reproduced as follows: \n",
        "1. The probability of an event A is between 0 and 1 (inclusive): $0 \\leq p(A)\\leq 1$\n",
        "2. The sum of the probability of all possible events (the *sample space*) is 1. $\\Sigma^n_{i=0} p(A_i)=1$\n",
        "3. The sum of the probability of an event and its complement is 1. $p(A^C)+p(A) = 1$\n",
        "4. (Addition Rule) The probability of event A *or* event B happening is equal to the sum of the probabilities of event A and event B happening respectively, *less* the probability of event A **and** event B. $p(A \\cup B)= p(A) + p(B) - p(AB)$\n",
        "5. (Multiplicative Rule) If events A and B are independent, then the probability of event A and B jointly occuring is the product of the probabilities of events A and B respectively. $p(AB) = p(A)p(B)$\n",
        "\n",
        "<div class=\"alert alert-info\">\n",
        "📝 <b>Note:</b> Events A and B are independent if the occurence of event A doesn't change the likelihood of Event B occuring. Do not confuse this with <b>mutually exclusive</b> events. If events A and B are mutually exclusive (disjoint), they cannot both happen. \n",
        "</div>"
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      "source": [
        "# What is Expectation?"
      ]
    },
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      "metadata": {
        "id": "3-D7OFb2Yr7P"
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      "source": [
        "In any set of possible events, we can compute the probability of each of those events. We saw that all events can happen with probability of 1/6. Or sometimes, you can have one event with probability 1/6 and another with 5/6.\n",
        "\n",
        "Now what if each of these outcomes was associated with a quantity. For eg. if you toss a coin and it's heads, you get Rs. 5. If it's tails, you lose Rs. 2. Will you play this game the coin is fair?\n",
        "\n",
        "Of course you will. Because you feel that on average you will get $\\frac{5 - 2}{2} = 1.5$ rupees as your winnings per round.\n",
        "\n",
        "But what if the coin is biased. It comes heads $\\frac{1}{6}$ of the time and $\\frac{5}{6}$ of the time it's tails. Now you might not be sure, so let's try to take the weighted average.\n",
        "\n",
        "$$E = \\frac{1}{6} \\times 5 - \\frac{5}{6} 2 = \\frac{5 - 10}{6} = -\\frac{5}{6}$$, so you are losing slightly less than a rupee every round, not a favorable game to play. This value, the weighted sum of the \"value\" of each outcome is called the expectation. Mathematically:\n",
        "\n",
        "$$E = \\sum_{i \\in S} P_i V_i$$\n",
        "\n",
        "Where S is the sample space, $P_i$ is the probability of the sample, and $V_i$ is the value associated with the sample. $i$ is each possible sample in the sample space."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TpEnGw-RaKhP"
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      "source": [
        "## Simulating to compute Expectation\n",
        "\n",
        "Let's test your basic coding skills:\n",
        "\n",
        "> You have a suffled deck of 52 cards, 4 of which are aces. You are to draw cards one by one and throw them out. As soon as you see an ace you stop. How many non-ace cards did you throw out?\n",
        "\n",
        "Whether or not you can solve this mathematically, try computing this numerically, that is by simulation in code. \n",
        "\n",
        "**Do not look at the solution given below.**\n"
      ]
    },
    {
      "cell_type": "code",
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        },
        "id": "kefyYq44US6f",
        "outputId": "f66a83ee-4201-46a1-bfda-129d3e8a5c47"
      },
      "source": [
        "def number_of_numbered_cards_drawn_before_ace(trials=100, show_trials=10):\n",
        "    values = ['A', '2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K']\n",
        "    ranks = ['H', 'D', 'C', 'S']\n",
        "    \n",
        "    cards_thrown_counts = []\n",
        "    for experiment in range(trials):\n",
        "        deck_of_cards = [value + rank for value in values for rank in ranks]\n",
        "        cards_thrown = 0\n",
        "        cards_pile = []\n",
        "        while len(deck_of_cards) > 0:\n",
        "            picked_card = np.random.choice(deck_of_cards)\n",
        "            cards_pile.append(picked_card)\n",
        "            if picked_card[0] == 'A':\n",
        "                break\n",
        "            cards_thrown += 1\n",
        "            deck_of_cards.remove(picked_card)\n",
        "        if experiment < show_trials:\n",
        "            print(cards_thrown, 'cards were thrown:', ' '.join(cards_pile))\n",
        "        cards_thrown_counts.append(cards_thrown)\n",
        "\n",
        "    return np.mean(cards_thrown_counts), cards_thrown_counts\n",
        "\n",
        "expected_cards_thrown, cards_thrown_counts = number_of_numbered_cards_drawn_before_ace(10000)\n",
        "print(f'\\n{expected_cards_thrown} cards are tossed before we see the first ace!')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "11 cards were thrown: 4C 7D 7C JS 2D JH 7S 8S 8H 4S JC AS\n",
            "9 cards were thrown: 7H 8S 8D QS KS JC 6D 10D 9C AS\n",
            "8 cards were thrown: JS 4C 8H 6D KD 6C 9C 5C AS\n",
            "3 cards were thrown: QS KC 2C AD\n",
            "7 cards were thrown: 6H 4S QD 3S 3D 9H 5C AH\n",
            "16 cards were thrown: 9C 4H 10D QH 6S 9S 5C 10S KD KH 3S 10H 7S 10C JC QC AS\n",
            "2 cards were thrown: 10D 9C AH\n",
            "26 cards were thrown: JD QS 4H 9S 4C 8D 8H KC 7H 10D KS 3C 8S 6S 6C 5D 7D 7S KD 4S 6H 3D 2C 9H 9D 2D AH\n",
            "0 cards were thrown: AS\n",
            "9 cards were thrown: JC QS 6D 3C 8C QH 5S 6H KD AC\n",
            "\n",
            "9.602 cards are tossed before we see the first ace!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5PVy5IwRj_Vs"
      },
      "source": [
        "## Visualize the Underlying Probability Mass Function"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tgp8NMf_dbsI"
      },
      "source": [
        "If you guess mathematically, you will guess that almost 1/13 cards are aces, so about 12 can be met on average before you see your first ace. And you won't be totally wrong.\n",
        "\n",
        "Of course the percentage of aces increases as you keep throwing away the cards, so the actual expectation is not that.\n",
        "\n",
        "Let's see the probability distribution for it!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "K1tK6czZixdv",
        "outputId": "2cdc9bb7-23ee-4a29-cc14-e4720436d37c"
      },
      "source": [
        "results = pd.Series(cards_thrown_counts)\n",
        "fig = pg.Figure([pg.Bar(x=results.value_counts().keys(), \n",
        "                        y=results.value_counts().values)])\n",
        "fig.show()"
      ],
      "execution_count": null,
      "outputs": [
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      "source": [
        "## A new trick - Technique of Contributions (Optional)\n",
        "\n",
        "The correct way to solve for this is not particularly relevant for this course. However, if you are interested, it's called the **Technique of Contributions**.\n",
        "\n",
        "You can say that if there was only 1 non-ace card, and 4 aces in the deck, the number of cards thrown would be $\\frac{1}{5}$, since if and only if the numbered card is the first one you pick do you throw away a card, otherwise it's 0. So the card contributes $\\frac{1}{5}$ to the answer, which it does if it's picked before any of the 4 aces.\n",
        "\n",
        "Now each of the cards are non-interacting, and there are $48$ non-ace cards, so our answer would be $\\frac{48}{5} = 9.6$\n",
        "\n",
        "This is exactly what we simulated."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZQxe6sW8PmeI"
      },
      "source": [
        "# Measurements and Errors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8MndZtI7ds-X"
      },
      "source": [
        "## Using Mean Squared Error"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x9xFz2uzdu6A"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VIPZteQrdyVd"
      },
      "source": [
        "Suppose you are measuring the height of a person. You have several students, each of whom take 2 readings.\n",
        "\n",
        "* Student 1: 4 feet and 8 feet.\n",
        "* Student 2: 4 feet and 4.5 feet.\n",
        "* Student 3: 6 feet and 6 feet\n",
        "* Student 4: 6 feet and 10 feet\n",
        "\n",
        "How will you rate these students?\n",
        "\n",
        "My estimate is that would would want to rank them as:\n",
        "* Student 3\n",
        "* Student 2\n",
        "* Student 1\n",
        "* Student 4\n",
        "\n",
        "This is because 3 is correct.\n",
        "2 is wrong, but he made a 2 foot and a 1.5 foot error.\n",
        "1 is worse, **even though his average is correct**, he messed up by 2 feet each time, so he should be penalized for his 2 feet errors and not let the 2 errors cancel each other out (we need absolute value of errors or square of errors to do this).\n",
        "4 is the worst, he has a bizzare 4 foot error. He got to 6 foot once, but that's just by chance, while others mess in 2 feet, his is messing up in 4 feet and is the least reliable. This shows that **outliers should be penalized more**."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "id": "ZWXGAh2fe3ip",
        "outputId": "aabe7115-a949-49a5-abca-0f87d78573b2"
      },
      "source": [
        "from matplotlib import pyplot as plt\n",
        "plt.style.use('ggplot')\n",
        "plt.figure(figsize=(10, 10))\n",
        "\n",
        "measurements = np.linspace(0, 12, 1000)\n",
        "plt.scatter(measurements, (measurements - 6) ** 2, label='Squared Error')\n",
        "plt.scatter(measurements, abs(measurements - 6), label='Absolute Error')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MSqnk0rJfVw_"
      },
      "source": [
        "You can see that the Mean Squared eror is a great penalty, because it punishes getting things too wrong a lot more."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cxTEEHWz3he7"
      },
      "source": [
        "## Standardisation\n",
        "\n",
        "We consider the grades dataset, which contains Physics, Biology and Maths scores for 26 students:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 161
        },
        "id": "mfXq7su73he8",
        "outputId": "8b8dbb52-c0d2-4d3d-c5de-35e76938bdca"
      },
      "source": [
        "grades = pd.read_csv(\"https://archive.org/download/ml-fundamentals-data/machine-learning-fundamentals-data/grades.csv\")\n",
        "print(grades.shape)\n",
        "grades.agg([\"mean\", \"var\", \"std\"])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(26, 4)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Physics</th>\n",
              "      <th>Biology</th>\n",
              "      <th>Maths</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>63.769231</td>\n",
              "      <td>67.038462</td>\n",
              "      <td>69.769231</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>var</th>\n",
              "      <td>517.224615</td>\n",
              "      <td>456.758462</td>\n",
              "      <td>300.664615</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>22.742573</td>\n",
              "      <td>21.371908</td>\n",
              "      <td>17.339683</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Physics     Biology       Maths\n",
              "mean   63.769231   67.038462   69.769231\n",
              "var   517.224615  456.758462  300.664615\n",
              "std    22.742573   21.371908   17.339683"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 242
        },
        "id": "IPtO3_G23he9",
        "outputId": "fdc014dd-2cba-4b4c-c885-e71f1acde9de"
      },
      "source": [
        "g = sns.FacetGrid(grades.melt(\"Name\"), col=\"variable\")\n",
        "g.map(plt.hist, \"value\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<seaborn.axisgrid.FacetGrid at 0x7ffa43f291d0>"
            ]
          },
          "metadata": {},
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x216 with 3 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lvidQTVn3he9"
      },
      "source": [
        "Suppose the instructor wanted to provide the students with an idea of how well they are performing relative to their peers, but not their exact score. This can be done by **standardising** the scores. This is done by subtracting the mean and re-scaling the data to be in units of standard deviations.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i7lo_TZr3he-"
      },
      "source": [
        "grades[\"Physics_std\"] = (grades[\"Physics\"] - grades[\"Physics\"].mean()) / grades[\"Physics\"].std()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "dgfwyX7G3he-",
        "outputId": "93140993-9d59-4026-9977-8f097845e851"
      },
      "source": [
        "grades.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Name</th>\n",
              "      <th>Physics</th>\n",
              "      <th>Biology</th>\n",
              "      <th>Maths</th>\n",
              "      <th>Physics_std</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Arnold</td>\n",
              "      <td>80</td>\n",
              "      <td>78</td>\n",
              "      <td>70</td>\n",
              "      <td>0.713673</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Bob</td>\n",
              "      <td>60</td>\n",
              "      <td>98</td>\n",
              "      <td>45</td>\n",
              "      <td>-0.165735</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Cassandra</td>\n",
              "      <td>34</td>\n",
              "      <td>56</td>\n",
              "      <td>65</td>\n",
              "      <td>-1.308965</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Donovan</td>\n",
              "      <td>56</td>\n",
              "      <td>65</td>\n",
              "      <td>32</td>\n",
              "      <td>-0.341616</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Emily</td>\n",
              "      <td>98</td>\n",
              "      <td>23</td>\n",
              "      <td>55</td>\n",
              "      <td>1.505141</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Name  Physics  Biology  Maths  Physics_std\n",
              "0     Arnold       80       78     70     0.713673\n",
              "1        Bob       60       98     45    -0.165735\n",
              "2  Cassandra       34       56     65    -1.308965\n",
              "3    Donovan       56       65     32    -0.341616\n",
              "4      Emily       98       23     55     1.505141"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u87UswSM3he_"
      },
      "source": [
        "What can we conclude? \n",
        "\n",
        "Firstly, Arnold and Emily are above average Physics students, whereas Bob, Cassandra and Donovan are below average. \n",
        "\n",
        "Also, Emily's scores are **1.5 standard deviations above the mean**, whereas Cassandra's scores are **1.3 standard deviations below the mean**. \n",
        "\n",
        "More importantly, standardisation allows us to compare the results from different exams. Standardisation allows each of the variables to be expressed in common units: their respective standard deviation. \n",
        "\n",
        "We can do the same for Math scores, which have a lower variance than Physics scores: "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "RcxIigBz3hfA",
        "outputId": "d6578d93-e2d4-4531-815c-eaa4b0fd4565"
      },
      "source": [
        "grades[\"Maths_std\"] = (grades[\"Maths\"] - grades[\"Maths\"].mean()) / grades[\"Maths\"].std()\n",
        "grades.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Name</th>\n",
              "      <th>Physics</th>\n",
              "      <th>Biology</th>\n",
              "      <th>Maths</th>\n",
              "      <th>Physics_std</th>\n",
              "      <th>Maths_std</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Arnold</td>\n",
              "      <td>80</td>\n",
              "      <td>78</td>\n",
              "      <td>70</td>\n",
              "      <td>0.713673</td>\n",
              "      <td>0.013309</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Bob</td>\n",
              "      <td>60</td>\n",
              "      <td>98</td>\n",
              "      <td>45</td>\n",
              "      <td>-0.165735</td>\n",
              "      <td>-1.428471</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Cassandra</td>\n",
              "      <td>34</td>\n",
              "      <td>56</td>\n",
              "      <td>65</td>\n",
              "      <td>-1.308965</td>\n",
              "      <td>-0.275047</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Donovan</td>\n",
              "      <td>56</td>\n",
              "      <td>65</td>\n",
              "      <td>32</td>\n",
              "      <td>-0.341616</td>\n",
              "      <td>-2.178196</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Emily</td>\n",
              "      <td>98</td>\n",
              "      <td>23</td>\n",
              "      <td>55</td>\n",
              "      <td>1.505141</td>\n",
              "      <td>-0.851759</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Name  Physics  Biology  Maths  Physics_std  Maths_std\n",
              "0     Arnold       80       78     70     0.713673   0.013309\n",
              "1        Bob       60       98     45    -0.165735  -1.428471\n",
              "2  Cassandra       34       56     65    -1.308965  -0.275047\n",
              "3    Donovan       56       65     32    -0.341616  -2.178196\n",
              "4      Emily       98       23     55     1.505141  -0.851759"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mZiauZze3hfB"
      },
      "source": [
        "What do we observe? \n",
        "\n",
        " - While Arnold is doing really well in Physics, he's barely above average in Maths. \n",
        " - Bob, Cassandra and Donovan are below average in both Physics and Maths. \n",
        " - While Emily seems to be an above average Physics student, she's quite the opposite when it comes to Maths. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lFu5zIBxPcL_"
      },
      "source": [
        "# Mathematics of Probability"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q7jqREao3hfD"
      },
      "source": [
        "## Conditional Probability \n",
        "|Sex/Handedness|Right handed| Left handed|\n",
        "|--------------|-----------:|-----------:|\n",
        "|Male          |43          | 9          |\n",
        "|Female        |44          | 4          |\n",
        "\n",
        "The contingency table above summarises some fake data collected from 100 respondents on genders and handedness. \n",
        "\n",
        "**What is the probability that any one respondent in our survey is female?** To calculate the probability, divide the number of events by the sample space: $\\frac{44+4}{100}=0.48$. It is a little more likely that our respondents are male than female. \n",
        "\n",
        "However, what is the probability that a female in our sample is **left-handed**? Quite unlikely. To quantify the likelihood, we could divide the number of left-handed females by the number of females in our sample: $\\frac{4}{48}=\\frac{1}{12}$. \n",
        "\n",
        "$\\frac{1}{12}$ is a **conditional probability**: a probability under a condition. Note that to calculate the conditional probability, we restrict the sample space under consideration to a condition, and then recalculate the probability as if the condition were the entire sample space. \n",
        "\n",
        "A general formula for conditional probability is as follows. The conditional probability of A given B is \n",
        "\n",
        "$$P(A|B)=\\frac{P(A\\cap B)}{P(B)}$$\n",
        "\n",
        "We take the joint probability $P(A\\cap B)$ and 'inflate' it with the probability of $P(B)$. \n",
        "\n",
        "Conditional probabilities are fundamental to the idea of **independence**. Recall that we defined independence of two events A and B as \n",
        "\n",
        "> the probability of event A is not changed by the occurence of event B. \n",
        "\n",
        "We can restate the definition above as \n",
        "\n",
        "$$P(A|B)=P(A)$$\n",
        "\n",
        "Consider whether handedness is independent of sex. The probability of being left-handed is $11/100$, or 0.11. As you might expect, it's close to the conditional probability $P(left$-$handed|female)=0.12$. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3U96C3_Q3hfD"
      },
      "source": [
        "## Law of Total Probability\n",
        "\n",
        "Let $A_1, \\dots A_n$ be mutually exclusive and exhaustive events, where $P(A)\\neq 0$ for all $A$. Then, the probability of $P(B)$ can be defined as \n",
        "\n",
        "$$P(B)=\\sum^n_{i=1}P(B|A_i)P(A_i)$$\n",
        "\n",
        "### Example \n",
        "\n",
        "The probability that any given person in the population has a disease is 0.1. The likelihood of testing positive for a disease if you have it is 0.95. The probability of testing positive in the absence of the disease (a false positive) is 0.10. \n",
        "\n",
        "What is the probability of testing positive for the disease? \n",
        "\n",
        "$$P(T = 1|D = 1) = 0.95$$\n",
        "$$P(T = 1|D = 0) = 0.10$$\n",
        "$$P(D = 1) = 0.1$$\n",
        "\n",
        "\n",
        "$$\\begin{align}\n",
        "P(T=1)&=P(T=1|D=1)P(D=1) + P(T=1|D=0)P(D=0)\\\\\n",
        "&= 0.95\\times 0.1 + 0.10*0.90\\\\\n",
        "&=0.14\n",
        "\\end{align}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yHVxSe4msYXP"
      },
      "source": [
        "## Bayes' Theorem\n",
        "\n",
        "$$P(A|B)=\\frac{P(B|A)P(A)}{P(B)}$$\n",
        "\n",
        "$$Posterior=\\frac{Likelihood\\times Prior}{Evidence}$$\n",
        "\n",
        "An informal way of putting Bayes' Theorem: \n",
        "\n",
        "$$P(pred|data)=\\frac{P(data|actual)P(actual)}{P(data)}$$\n",
        "\n",
        "The proof for Bayes' Theorem follows from the definition of conditional independence. We know that \n",
        "\n",
        "$$\\begin{align}\n",
        "P(A\\cap B)&=P(A|B)\\times P(B)\\\\\n",
        "&=P(B|A)\\times P(A)\n",
        "\\end{align}$$\n",
        "\n",
        "This can be rearranged to state Bayes's Theorem: \n",
        "\n",
        "$$P(A|B)=\\frac{P(B|A)P(A)}{P(B)}$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fHOTHeSp3hfE"
      },
      "source": [
        "**Example 1**\n",
        "\n",
        "You want to go for a picnic today but it is cloudy in the morning. From experience, you know that:\n",
        "\n",
        "- the probability of raining on any given day is 10%, \n",
        "- the probability that it is cloudy on any given day is 40%, and \n",
        "- 50% of all rainy days start off cloudy. \n",
        "\n",
        "What is the probability of raining given that it is cloudy?\n",
        "\n",
        "$P(Rain | Cloud) = \\frac {P(Cloud | rain) \\times P(rain)}{P(Cloud}=\\frac{0.5\\times 0.1}{0.4}=0.125$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "18gxjKv-3hfE"
      },
      "source": [
        "**Example 2**\n",
        "\n",
        "The probability that any given person in the population has a disease is 0.1. The likelihood of testing positive for a disease if you have it is 0.95. The probability of testing positive in the absence of the disease (a false positive) is 0.10. \n",
        "\n",
        "If you have been tested positive for a disease. What is the probability that you actually have the disease? \n",
        "\n",
        "What is the probability of actually getting the disease given tested positive?\n",
        "\n",
        "$$P(T = 1|D = 1) = 0.95$$\n",
        "$$P(T = 1|D = 0) = 0.10$$\n",
        "$$P(D = 1) = 0.1$$\n",
        "\n",
        "As we've done earlier, we can use the law of total probability to find $P(T=1)$: \n",
        "\n",
        "$$\\begin{align}\n",
        "P(T=1)&=P(T=1|D=1)P(D=1) + P(T=1|D=0)P(D=0)\\\\\n",
        "&= 0.95\\times 0.1 + 0.10*0.90\\\\\n",
        "&=0.14\\end{align}$$\n",
        "\n",
        "Note that $$P(T = 1|D = 1) = 0.95$$ is the likelihood and $$P(D = 1) = 0.1$$ is the prior. \n",
        "\n",
        "\n",
        "$\\begin{align}\n",
        "P(D=1|T=1)&=\\frac{P(T=1|D=1)P(D=1)}{P(T=1)}\\\\\n",
        "&=\\frac{0.95\\times 0.1}{0.14}\\\\\n",
        "&=0.68\n",
        "\\end{align}$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tK13xYcvshUg"
      },
      "source": [
        "## Random variables \n",
        "- A **continuous random variable** takes on infinitely many values/real numbers. In fact, the probability of a continuous random variable taking on any one value is 0. \n",
        "- A **discrete random variable** takes on a finite set of values, e.g. counts."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-uCXypFm3hfE"
      },
      "source": [
        "## Probability Distributions \n",
        "A random variable is a variable whose possible values are the outcomes of a non-deterministic process."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9v6WE4xZslqY"
      },
      "source": [
        "### Binomial distribution\n",
        "\n",
        "We start with the **binomial distribution**. The binomial distribution models the probability of $k$ successes in $n$ independent trials. \n",
        "\n",
        "Let's redo the lecture example with `scipy`. Import the `binom` class from `scipy.stats`: "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AW7zhBam3hfG"
      },
      "source": [
        "from scipy.stats import binom"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X4W_VnSM3hfG"
      },
      "source": [
        "If the chance of winning a game is 0.75, what is the probability of losing all 5 games?\n",
        "\n",
        "Assume the chance of winning each game is independent. Then we can solve this problem using the binomial distribution. \n",
        "\n",
        "We use the `.pmf` method of the `binom` class. `pmf` stands for **probability mass function**: a function that states the probability that a discrete random variable is equal to any one value. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PeB5cBkp3hfG",
        "outputId": "3f6a85c9-8165-4775-848f-1195f67f4eb0"
      },
      "source": [
        "binom.pmf(k=5, n=5, p=0.25)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0009765625"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gS5bOH9F3hfH"
      },
      "source": [
        "The answer is what we should expect. If we win 3 in 4 games, it's unlikely we lose 5 in 5 games. \n",
        "\n",
        "Now, suppose we want to know what is the probability of winning 3 games or less. We want to find $P(X \\leq 3)$. \n",
        "\n",
        "Note $P(X \\leq 3) = P(X=0)+ P(X=1)+P(X=2)+P(X=3)$. \n",
        "\n",
        "By the **complement rule**, $P(X \\leq 3) = 1 - P(X=5)-P(X=4)$. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hquniyy63hfH",
        "outputId": "e2d24232-0946-4ae8-cdd9-ac57459de5f2"
      },
      "source": [
        "1 - binom.pmf(k=4, n=5, p=0.75) - binom.pmf(k=5, n=5, p=0.75)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.36718749999999994"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JjPx-QQy3hfH"
      },
      "source": [
        "Note that we could also answer this by referring to the value of the **cumulative density function** at $X=3$. \n",
        "\n",
        "The cumulative density function, $F(x)$, is defined as \n",
        "\n",
        "$$F(x)=P(X\\leq x)$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZCgi1f1x3hfH",
        "outputId": "c0bad055-3378-4236-e330-8a1b16213ae5"
      },
      "source": [
        "binom.cdf(3, n=5, p=0.75)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3671875"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iX_F-Cbb3hfH"
      },
      "source": [
        "### Normal distribution\n",
        "\n",
        "We move on to the **normal distribution**. There are some key properties that are important to know about this distribution: \n",
        "\n",
        "- The mean, median and mode of the distribution is the same.\n",
        "- The curve is bell-shaped.\n",
        "- The total area under the curve is 1.\n",
        "- Symmetric about the mean.\n",
        "\n",
        "There are two key **shape parameters** that define the location and spread of the normal distribution: the mean, commonly denoted as $\\mu$; and the standard deviation, commonly denoted as $\\sigma$. \n",
        "\n",
        "Again, start by importing the `norm` class from `scipy.stats`: "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2xVbMbX53hfI"
      },
      "source": [
        "from scipy.stats import norm"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ELt3TEjr3hfI"
      },
      "source": [
        "#### Standard normal distribution\n",
        "\n",
        "A normally distributed random variable with mean 0 and standard deviation 1 is said to follow the standard normal distribution, also known as the **z-distribution**. \n",
        "\n",
        "A normally distributed random variable can be converted into the standard normal distribution by standardisation: \n",
        "\n",
        "$$Z = \\frac{X-\\mu}{\\sigma}$$\n",
        "\n",
        "<div class=\"alert alert-info\">\n",
        "    <b>Note:</b> The <code>.pdf</code> method refers to the <b>probability density function</b>, which is the counterpart of the probability mass function for continuous random variables. \n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "lfkKKZl-3hfI",
        "outputId": "3128da11-fe8a-4be8-cfc0-98ed4e83f3bf"
      },
      "source": [
        "x = np.linspace(-10, 10, 100)\n",
        "f1 = norm.pdf(x, loc=0, scale=1)\n",
        "f2 = norm.pdf(x, loc=1, scale=1)\n",
        "f3 = norm.pdf(x, loc=0, scale=2)\n",
        "\n",
        "plt.plot(x, f1, label=\"$\\mu=0, \\sigma=1$\")\n",
        "plt.plot(x, f2, label=\"$\\mu=1, \\sigma=1$\")\n",
        "plt.plot(x, f3, label=\"$\\mu=0, \\sigma=2$\")\n",
        "plt.vlines(x=0, ymin=0, ymax=0.5, linestyles=\"dotted\")\n",
        "\n",
        "plt.legend()\n",
        "plt.title(\"$\\mu$ and $\\sigma$ affect the shape of the normal distribution\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jSE9Px4IFCwbsnJ54TAYpKSmorq5GXV0drFYrDh8+jKysLKd9mpqaHP8/evRor85lQoaLtWvX4i9/+ctgh0EGgM1mw7PPPoutW7di//79+OSTT3D27NkBOfcdd9yBv//97wNyLm95TAZisRhLly7FunXr8Nhjj2HmzJnQ6/XYvn07jh49CgD4/PPP8fjjj+OJJ57A559/jgcffDDggRMSCOPHj8ekSZMGOwziwa233ori4mIA9n5NX35h5+bmYsyYMUhMTIRMJsPNN9+M3bt391kmPz8fP/vZzzBv3jzEx8cjLi4Of/zjHwWfe+bMmQgNDRVcLpC86jPIzMxEZmam07bFixc7/n/nnXfizjvv9G9khAyCnJwchIaGIi0tbbBDGfL4//c2WEWZ/f8cB3+sk8XpkyC64z6P+5WVlSE5ORkAcPr0aYwfP97p8Z/+9Kdob28Hd1lczz33HK655hoAQE1NjVP7e0xMDHJzc92e02g0Yvny5diwYQOmTZuGl19+GSaTCb/5zW96nfdyPc87VA3NbnZCBslLL70EqVSKbdu2DXYoxI3KykrExMRAJLI3bJw+fRoTJkxw2udf//oXAP92IH/zzTeYMmUKpk2bBgCYMGECvvrqK6d7AbrPOxxRMiCkh/Xr1yMsLGywwxgWev6CH8hROwUFBU5f/idOnMBPfvITp328qRlER0c7ralSXV2N6Ohot+ctLCx0qoGcOnUKU6ZMcXney1HNgJBhJjU1ddCHb5K+5efnw2g0AgBKS0uxZ88erFq1ymkfb2oGU6dORVlZGcrLyxEdHY2dO3di48aNjsdvv/12bNiwATExMQCAsLAwHDp0CABQUlKCXbt2YefOnS7POxzRFNaE9HDkyBEcOHBgsMMgfSgoKABjDNnZ2Xj11VeRlpaGf/7zn4KPI5FIsHbtWtx5552YN28ebrrpJowbNw6AfRqec+fOOXXy3nLLLejo6MCCBQuwatUqvPnmm72G2Xtr2bJl+MlPfoKSkhJMnz59SDRLUs2AkB7+9Kc/UZ/BEFdQUIDdu3cjODi438dauHChy0k1z549ixtuuMFpxtCgoCC8//77/T4nALz11ltD7mY4SgaE9PCnP/2J+gyGsO5+AH8kgr6MHz8ea9asCeg5hhpqJiKkh8TERMeQRTL0BAcH4+DBg4MdxohENQNCejhw4AA0Gg0yMjIGOxRCBhQlA0J6eO2116jPgIxKlAwI6WHDhg0+jxAhZDijPgNCeoiLi4Nerx/sMAgZcFQzIKSH/fv3Q61WY/r06YMdCiEDipIBIT1s3LiR+gzIqETJgJAe+nNXKSHDGfUZENJDZGRkn5OVETJSUTIgpIc9e/bgs88+G+wwyAB5/PHHB2X5yWG57CUho8mmTZuwYcOGwQ6DDJDbb799UJafHJbLXhIymmzatIk6j4cBfyx7CQBXXXWVoOUnR/2yl4SMFlqtltYz8NLfjtairMm+rsDli8j4KilMgXuzojzu549lL4WiZS8JGUV27doFtVqNOXPmDHYoxA1a9jIwKBkQ0sM777wDqVRKycALPX/BD8dlL4WiZS8JGUXeeecd6HQ6WCyWwQ6FuOGvZS89oWUvCRnF1Go1NBrNYIdB+uCvZS8B4MEHH3S5/CQte0nIKLdz506o1WrMnz9/sEMhbvhz2cs333zT5XZa9pKQUW7Lli2QSqWUDIYoWvYycCgZENLDli1boNPp0NnZOdihEBdo2cvAoT4DQnpQKpVQqVSDHQYhA45qBoT08NFHHyEkJASLFi0a7FAIGVCUDAjpYdu2bZBKpZQMyKhDyYCQHrZt24bw8HC0tLQMdiiEDCjqMyCkB6lUCqlUOthhEDLgvEoGeXl5ePTRR/HrX/8an3zyidv9vv32W9x+++0oKSnxW4CEDKTt27fjgw8+GOwwCBlwHpMBz/PYvHkznnnmGbz66qs4dOgQKisre+3X1dWFzz//HGlpaQEJlJCBsGPHDmzZsmWwwyBkwHlMBsXFxYiOjkZUVBQkEglmzZqFnJycXvtt374dN998M1WxybD24YcfYu/evYMdBiEDzmMHcmNjI3Q6neNvnU6HoqIip31KS0vR0NCAzMxMfPrpp26PtW/fPuzbtw8AsH79eoSHh/sWtETic9lAoriEGWpxte94F+bjR9HEcRAxBvkVsxF0851elf2m1IDXvi5FqFKK8GA5xkYEYUlWPCRi/3bLDfZrVltbC4nE9deGu+2Dra+4/vvf/2L16tWw2Wz45S9/iUceeSTg8Vy4cAEPP/wwGhoawHEcfvWrX+H+++93ua9cLh+w693vq8fzPD744AM8+OCDHvfNzs5Gdna2429fFxAZqouPUFzCDKW4WHUl+G1/Q4syBFaFCjqJCJYtf0Xn+GngdBF9lrXyDBu+KoXVxiATSVBa34YDJQYEcRYsSPbvpHeD/ZqZTCaIxeJe2wdyCmsh+orLZrPhqaeewrZt2xATE4MbbrgB2dnZGDt2bMDjeuGFFzBx4kS0t7fj+uuvx5w5c1ye12Qy9bresbGxAYnJ488WrVYLg8Hg+NtgMDjN1Gc0GlFRUYEXXngBDz30EIqKivDyyy9TJzIZVtiuHYBUhidrzXj8QidEj79o3/7FRx7L7i9tQXWbBfdfEYUXFujxxo+TkKiR418FBvB+WP2L9OaPZS9zc3MxZswYJCYmQiaT4eabb8bu3bv7LOOPZS+joqKQnp4OwD69RlpaGmpqagTH728eawYpKSmorq5GXV0dtFotDh8+7FSVUqlU2Lx5s+PvNWvWYMmSJUhJSQlMxIT4GaurAvvua3DX/gR/u22p49c3N2sB2ME9YDfcBi5M57KsxcZj+8kGpOkUuCLOPnkax3H42SQtXj1cjaMX2jEjPmQgn86AOXWsE63NNgD+W/ZSHSrG5EzP04H4Y9nLmpoap1/ZMTExyM3NdXvOQCx7WVFRgVOnTjlWTxtMHpOBWCzG0qVLsW7dOvA8j/nz50Ov12P79u1ISUlBVlbWQMRJSMCwXR8CEgm4RT912s796FawQ/vAdn8M7o77XJbdW9KC+k4rHr4qxmn5w6sT1fj78QZ8lN84YpPBYBkpy152dHTgvvvuwwsvvICQkMF/j3jVZ5CZmYnMzEynbYsXL3a572ib9pUMb6yhFuzb/eDm3QBOE4b33nsPwcHBuPXWW8FFRIO7aj7Ygd1gP7oVnCbMqazJyuOfpwyYFKlERrTzr1mxiMMtE7TYdLQWBXWdmBg58ia/6/kLfjguexkdHY2qqirHY9XV1YiOjnZ7Xn8ue2mxWHDffffhpz/9KW644QZPT3lADM3uf0IGCPv8I4DjwF33MwD2EW9SqRS33norAIC74TawI/vB9nwC7rb/dSq7r6QFTV1WPDE71unXYbfsFA3+38kGfJRvGJHJYLD4a9nLqVOnoqysDOXl5YiOjsbOnTuxceNGx+OBWvaSMYbHHnsMqampWLZsmZfPOvBoOgoyajGrBey7r8BdOc/RJ7B161b8+9//duzDRcWCy5wJduS/YDzvVP77C+3Qa2SYFOX6i14uEeGmcWE4WtWBC63mwD2RUcZfy15KJBKsXbsWd955J+bNm4ebbroJ48aNAxDYZS9zcnKwY8cOHD58GNdeey2uvfZafPnll4KP429UMyCjV1kRYDKCS7+i7/3Ss4AfDgFV54H4JACA2cajoK4T16WG9ll0bpIafz/RgLzqDsSpZf6KfFTz57KXCxcuxMKFC3ttD+SylzNmzEBtbe2QG4pLNQMyarHTxwGOA8ZNdmz729/+htdff91pP258+sX9Tzi2nanvgtnGMDUmqM9zRAXLEBkkxYnaDj9GPnrRspeBQ8mAjFqs8ASQkAIu6NJIjoMHD2L//v1O+3HaCCAy1p48Ljpe0wkxB0yMVMKT9GgV8ms76Z4DP6BlLwOHkgEZlZjJCJQUOn71d3vvvffw8ccf99qfm5AOnM0Hu1i1P17TgXHhSqikve/GvdyUKBXazDzONZn8EzwhAUDJgIxOxacBm7VXMnCHG58OmLqA88VoN9lQ0mhERnTfTUTdplzsYD5Z2+lzuIQEGiUDMiqx08cBsQRIm+i0/a9//Sv+/Oc/9y4wLt1R7mRtJ3iGXvcWuKNTSREbIsPJEdBv4I+7jIn3BvL1pmRARiV25gSQMg6cXOG0/YcffsB3333Xa38uRA3ok8DOnMDxmg4oJCKkhXvuL+g2JUqF/Lou2Pjh/WUqEomG3CiYkcpqtTrush4INLSUjDqsox0oLwH34zt6Pfb222+7nRmUG58Otn8Xjqe1Y0qUEhJR7xvN3JkSpcLu4maUNBoxVkASGWoUCgWMRiNMJpPTjXZyuRwm09DrExmucTHGIBKJoFAo3O7jb5QMyOhTeBJgDNyEDEHFuAkZqD3wNararbhhnLCbjXr2GwznZMBxnNPY+26DPbW2OxSX96iZiIw67MwJQK4Aknov0frGG2+4n5I4bSJO6uxzznvbedwtVClBgkZGnchkyKKaARl12JkTQNpEcJLeS7Tm5+dDLpe7LMcpVMiPy4DG1gW9RvjdxFOiVNhX0gKLjUEq9r6JiZCBQDUDMqqwznagugJc2iSXj//f//0ftm7d6rZ8aXAcUpvPAz50ok6JCoLJxlDc2CW4LCGBRsmAjC4VZQAALkH44ksmK49KpkRSW6V9niKBxkXY29qLDUbBZQkJNEoGZFRh5aX2/yQku3z81Vdfxe9//3uXj51vNoEHh+T2C5eOI0CYQgyNQoxSuhOZDEHUZ0BGl/JSIFQLTu16ttHS0lK3fQYljfZf9Mlmg/04AnEch+QwBcqaqGZAhh5KBmRUYRWlgN51rQAAXn/9dbfD/kqbjAiRiRARpbUfxwfJYXLsPNNBnchkyKFmIjJqMLPJ3nnsponIk9JGE5K0CogSUoCKMjDeJvgYSWEKWHmgooWaisjQQsmAjB4XzgM832fn8R//+Ee88MILvbZbeYZzzSakhCns/Q1mE1BbLTiEZK39jtJSaioiQww1E5FRw1PnMQBUVVW5nAKgosUEK8+QrFWAkySDAWDlJeBi4gXFEBMihULCUScyGXIoGZDRo7wUUAUDuki3u7z66qsu+wwcncdaOaDSAxKp/XhXzhUUgojjMCZUgbJGqhmQoYWaicioYe88TnKaYM1bpU0mKCQixIbIwEkkQFyi753IWjlKm0y08hkZUigZkFGB2WxA5TmPncd/+MMfsHr16l7bSxuNSA6TQ3QxkXAJyUB5qU/zzSeFKWC08qhpswguS0igUDIgo0NNJWAx99lfAABNTU0wGAxO22w8Q1mTEUnaHn0J+mSgow1oFD7zZHKY/Th0vwEZSqjPgIwK3Z3HnL7vaShefvnlXn0G1W1mGK0MKWGXbkbjEuydyKgoAXQRgmJJCJVBzNmbnmYnCipKSMBQzYCMDuWlgEwGRMcJLto98ielZ80gfgzAicDOC+83kIlFiNfIUUqdyGQIoWRARgVWXgLEjQEnFve53+9+9zusWrXKaVtJoxFSEYd4TY+agVwBRMf1605kaiYiQwklAzLiMcaAijKv7jw2Go3o6nKeYvpckxEJobJey1xy+mSf5igC7DefNRltaOqi9YTJ0EDJgIx8jQ1AVwcQn+Rx19///vd47bXXnLaVt5iRoHExeZ1+DNDUYF9TWaCki/0P1FREhgqvOpDz8vLw7rvvgud5LFy4ELfccovT43v27MHu3bsdCzgvW7YM8fHC7swkJGCqygEAXGyC4KLtZhsau6zQu0gGXGyCvRO5uhxInSjouGNC7f0P51tMmB4XLDguQvzNYzLgeR6bN2/G6tWrodPp8PTTTyMrK8vpy37OnDlYtGgRAODo0aN4//338eyzzwYuakIEYNX2ZIBYvcd9n3/+eSiVSjz99NMALk0o57JmEGM/HquqACcwGYTIxQhTiFHRYhZUjpBA8dhMVFxcjOjoaERFRUEikWDWrFnIyclx2kelUjn+bzQafbrDk5CAqSoH1KHggtWCi3Z/WSeEuljzWBcJyOSOmodQeo2cZi8lQ4bHmkFjYyN0Op3jb51Oh6Kiol77ffHFF/jPf/4Dq9WK559/3uWx9u3bh3379gEA1q9fj/DwcN+CltxSNcYAACAASURBVEh8LhtIFJcwAxVXY30NuMQUhHlxrjfffBMSiQTWi2sc1+W3QiERYUJijOPu454MCUkQNdR4dezLjY1uwX8KaqHT6bz+ATXar6VQFJf3/HbT2fXXX4/rr78eBw8exEcffYSHH3641z7Z2dnIzs52/O1qARFvuFt8ZLBRXMIMRFyMMfDlpeBmLvD6XD3jKqppRpxahsbL7kruxkfEwHr6uE/PI1zGo8vC40x5DSKCpIJjG0ooLmH6E1dsbKyfo7Hz2Eyk1Wqdbs83GAzQarVu93fVjETIoGlsAIxdgJedx8888wweeeQRx9/2kUQumoi6xSYAzY1gncJHFHX3Q5Q3U1MRGXwek0FKSgqqq6tRV1cHq9WKw4cPIysry2mf6upLi3wcO3YMMTEx/o+UEF9Ud48k8tx5DAAKhQJKpRLApZFELjuPL+JiLiaZqgrBoelD7cetaKVkQAafx2YisViMpUuXYt26deB5HvPnz4der8f27duRkpKCrKwsfPHFFzh58iTEYjGCg4Px0EMPDUTshHjEujt3vawZPP/8844qfHfnrqthpQ6x3SOKysGlThAUm1ouhoZGFJEhwqs+g8zMTGRmZjptW7x4seP///u//+vfqAjxl6oKIETj/5FE3bpHFFULrxkA9qYiaiYiQwHdgUxGNFZV7nWtAACefPJJLF++HIC9LV8u5vrs3OVEIiBGf6kGIpBeI0NFi9mndREI8SdKBmTEYowB1RWC7jwOCwtzDKWuaDEhXiN3OaS0Jy5W71OfAWBvguqy8jDQHEVkkNF6BmTkauoeSeRd5zEAPP30044+g/IWMzKiVZ4LxSQAR/aDdbaDUwmbWqLniKJwlXfDSwkJBKoZkJHLD3MS9TWSqJvj+L6MKLo4bJU6kclgo2RARizW/eUc430yeOyxx3Dfffeh4mKnbkKo52TgGFHkQyeyRiGBRi6maSnIoKNmIjJyVZXbRxKFeD+SKDY2FiqVChWt9l/q+r5uOOumi7SvotaPTuRyqhmQQUbJgIxYrLpC0EgiAHjiiScQHh6O9V/kexxJ1I0TiYBo/aWaiEB6jRwHzrWCMUaTPJJBQ81EZES6NJLI+87jnrwdSdSNi03o1+ylHRYejTSiiAwiSgZkZGoyAF2dgvoLAODXv/417r77blS0mL1rIuoWmwA0G8A6OwQGSp3IZGigZEBGphp7k43QmkFycjKSx06AocsKvdqLzuOLuJiLiz3VVAo6H3BpeCl1IpPBRMmAjEis+uKXcrSw5Vcfe+wx3Lb0QQBAvJCawcXzOM4rgEYhRrBMRDUDMqgoGZCRqboCUAUB6lDBRc81dQIA4tUCkkFENCCR+DRHEcdxiFfLUUmzl5JBRKOJyIjEqiuBGL3g0TnLly9HR8rVEMdmIjrE+2TAicVAZCyYD81EgL0WklMpfE0EQvyFagZkZKquACewiQgAJk2aBGXUGMSEyCARCRzmGRPv8+yleo0MLSYbWk02n8oT0l+UDMiIwzragLYWIEb4sNKHH34YUm2csJFEF3ExeqC+FswivO0//mJndSV1IpNBQsmAjDwXf507RvgIYLExVLV0Ob6cBYmOBxgP1FYJLtqdfCpbqROZDA5KBmTEcYzo8aFmcP/jT8HGBI4kuojrPp8P/QYRQVLIxBzVDMigoWRARp6aSkAqA3QRgosmTrkCgIelLt2JigM4zqfhpSKOQ5xaRjUDMmgoGZARh1VXAlGx4ERiwWUnXjkPABAnZFjpRZxcDmgjfO5EjlfL6F4DMmgoGZCRp7riUpONQBWtZkSFyKGQ+PjRiNH7VDMAgHiNHPUdFpisvG/nJqQfKBmQEYWZTYChTvCdx90OnTiLpvOFPp+fi4kHai+A8cKHiOrVMjAAF6ipiAwCSgZkZKm5ADDmU+cxzxhYSATGaL1Y6tKdGD1gMQOGesFF42mOIjKIKBmQEYX1Y1hpfYcFPCfGLQtm+Xx+x3l96DeIDZFCxNHwUjI4KBmQkaWmEuBE9pE9AlVe7LxN1Cp9P39M9xKYwvsNpGIRooOllAzIoKBkQEaW6kogIgqc1PMKZZfr/hJ+9tf3+Xx6LigECNH4dK8BYG8qonsNyGCgZEBGFFZT6XPncWWrCTJmwU2LFvQviJh4R3OVUPFqGarazLDxrH8xECIQJQMyYjCbDai94FN/AWBvJkqNVOOBBx7oVxxctB6orrQvvSlQvFoGKw/UtFv6FQMhQlEyICNHQy1gtfo0kogxhooWk293Hl8uJh7obAfamgUX7R5RRE1FZKBRMiAjR7V9QXpfbjhrMdrQZubx5b/+geuvv75fYTiW2qwS3lTkWA+ZOpHJAKPFbciIwS7YkwEErnsMAOUXf4nPnpKKlJkp/QskNsEeT1U5uPHpgoqqpGLolBK614AMOEoGZOSorgC04eAUwm8a654T6O6f3YCx+mg0NDT4HodGCyiDfF/oJlROyYAMOK+SQV5eHt59913wPI+FCxfilltucXr8s88+w5dffgmxWAy1Wo3ly5cjIkL4jJGE9AerKnf8KheqvMWEIJkIYQrhk9tdjuM4IFZvj8cHCRoZvijqBM8YRAKX7STEVx77DHiex+bNm/HMM8/g1VdfxaFDh1BZ6TyGesyYMVi/fj1eeeUVXHXVVdi6dWvAAibEFcbbgJoLvk9Q12JCgkaO2267Dddee22/4+FiE3zqMwCABI0cZhtDLY0oIgPIYzIoLi5GdHQ0oqKiIJFIMGvWLOTk5DjtM3nyZMjl9lEQaWlpaGxsDEy0hLjTUGufE8iHmoHVyqOrmWEyr8Kdt/0Wv7zttzhxtBNn840w1FvB23wY8x+rB9pbwVqFjyjS0xxFZBB4bCZqbGyETqdz/K3T6VBUVOR2///+97+YOnWqy8f27duHffv2AQDWr1+P8PBwofECACQSic9lA4niEsafcRlLT6MFQNjEdEi9PGZDvRHHjzbhwvlOLOBDgRZAoRwDjgNqq2wwdpkvxskhfkwQMrLCoNV5N/TUNH4KmgFoOlshS04V9FymhlgBnIfB0vv1GQ3X0p8oLu/5tQP5wIEDKC0txZo1a1w+np2djezsbMffvnbShYeH96+DL0AoLmH8GRd/5hQAoFkZAs7DMVubbSg8ZUTNBQukMg6qaA4flTfif6+OwJRoOcLDw9HS0gKziYeh3oqGWisqz7fjXHE7YhOkGDdZgeCQvvsWWJDGHs/pkxBFC6+t6FQSnKlqQkOD8zxJo+Fa+tNIjCs2NtbP0dh5TAZarRYGg8Hxt8FggFar7bXfiRMn8K9//Qtr1qyB1Id5YQjpl+6RREr3I4kYYyg9a8Lp40aIJcDYSQokj5VjT1kzys+bkKiT4xe/+AWkUim2bdsGmVyEmHgZYuJlGDdZgZJCE8qKTKiptGDSNCUSU2T2zmJXQi+OKOpHv0E5NRORAeQxGaSkpKC6uhp1dXXQarU4fPgwHnnkEad9ysrK8Pbbb+OZZ56BRqMJWLCEuMOqyvu889hs4pH3fSdqq6yIjpMi4wolZHJ7l1lFiwlBUhG0Sgl+8YtfICQkpFd5mVyECelKJI+VI/e7Tpz8oQuGeivSs1SQSnsnhP6OKNJrZMiv64SNZxCLaEQRCTyPyUAsFmPp0qVYt24deJ7H/PnzodfrsX37dqSkpCArKwtbt26F0WjEn//8ZwD2KtCqVasCHjwhwMWRRNWV4MZNcfl4R5sNR77ugLGLx6RpSiSlOf+ir2gxIV4jB8dx+PnPf95nFV6uEOHKa4JQfMaEwpNGtDS14aq5wVAF9R6LwcUmgOV+69Nz6h5RVNdhQUyI8PWYCRHKqz6DzMxMZGZmOm1bvHix4//PPfecf6MiRIiGOvtIIhc1g7YWG4581Q7GgNkLghGm6/2Wr2gxY0Z8MACgq6sLnZ2dfZ6O4zikTVBAq5Pg+4PtOPzfNsycH4yg4Mv6EWL0wDd7wNpawIUIqzEnhNo7qstbTJQMyICguYnI8HexKYa7bFhpS5MNh/e3AwBmzXedCFqMVrSYbI7hnEuWLMHNN9/s1Wl1kRLMnBcMqxU4/N92tLU6r3vsiMeHpiLHHEXNNEcRGRiUDMiw51g7oEcy6K4RiMTArAXBCNG4Hv3TPQ1F9y/xJUuW4P777/f63KFaCWbNDwbP2xNCR3uPhOCYo0h4J7JKKka4SkKdyGTAUDIgw19VORB2aSSRsYvHdwfaIRIBs+cH9zkMtPvLtvuX+M0334zbbrtN0OnVoWLMWhAMxoDvDnTAbOLtD4RqAaXKp5qBPSaao4gMHEoGZNhjVRWOmUqtVobvv+mA2cQw4+ogqC5vx79MRYsJKqkIOqW9Cam1tRUtLS2CYwhRi3HFnCB0dfDIOdQBm41dHFGU4POqZwkaGSpbadUzMjAoGZBhjfE8UFMBLiYBjGc4dqQDLc02TJ8VhFCt5/ER5S1m6DWXRhctXboUt956q0+x6CIkmHqlCo31Nhz/vhOMMftcSb5OWBd6aUQRIYFGU1iT4a2hFjCbgVg9CvONqK2yYnKmElGxnm98ZIyhotmEKy6OJALsyUCtVvscTlyCDJ0dPM6cMEITZkJSbAJwcK9PI4q6O7XLm2lEEQk8qhmQ4a3qPACgPigVRQUm6JNkSErzbv6gJqMNLSYbxoRe2v+GG27oNUW7UKnj5YiJl+L0CSMaNWn2jRfOCz6OY0RRC40oIoFHyYAMa6ziHLqU4cg9p4VaI8LkTKXnQheVNRoBAMlhCse2xsbGfs9lw3EcMmaooAoS4VhVDEwyDVhlmeDjqKRiRKgkONds7Fc8hHiDkgEZ1mwV53Bs2mNgAKbPDoJE4v3UDWXN9pE6iWGXagb3338/fvGLX/Q7LqmUQ9bsIFisHPKm/hp8+TmfjpOkVaCsiUYUkcCjPgMyrJ21jUOLSo/pV6g8ziR6uXNNRkQGSRAsu1Tu/vvv71efQU/qUDHSp6uQ9/1YlNRXYJwPx0gKk+PohXaYrDzkEvrtRgKH3l1k2GqoaEdpxFwkSCoQqxfewVrWZMKYHk1EALBo0SL8+Mc/9leI0CfJEMtVokg3F031wpt7ksIU4BlwvplqBySwKBmQYcli5pF31AhVZx0mpgj/ojRZeVS1mZEU5tzZXFdXh5qaGn+FCQCYHN8MubkFuYc7YLUKu2cg+WJ81FREAo2SARmWTh7rgtEsxtT8v0KSmCS4fHmLCTwDkkKdawYPPvgglixZ4q8wAQCypERk5G9Ch1GEgrwuQWUjg6RQSUUoa6JOZBJY1GdAhp2qCjMunLdgrPUEQvkG+7QPAnX/0h5zWc3goYce8lufgUNULHQdJUhCEcpKxiIqToqoGO8WgOI4DklhcpRSzYAEGNUMyLBiMvI4+UMXNGFiJJd9CuiT3K821odzTUYoJCJEBTt/Kc+fPx/XXXedv8IFAHAiMRCbiLGV/0GwWoQTOZ2wmL1vLhoTpsD5ZiN4RtNSkMChZECGlVPHumC1MGRkySG6cA6cXngTEXCx8zhUDtFlieTChQuoqPBtLqG+cPokiCuKkXGFEkYjQ8Fx75uLksPkMFoZatpoWgoSOJQMyLBRVWFGVYUFaZMUUBtrAKsFiBeeDBhjONds6tV5DACPPvooli5d6o9wnemTgI42hImakTpOjvJSM+pqvPtyT7o44on6DUggUZ8BGRZMpkvNQ6nj5WA59jt6fakZ1HVY0GnhHV+yPT3yyCMBWceb0yeBAUDFOYydnIWaCxYcz+nEvOvVLtdQ7kmvkUHMgfoNSEBRzYAMC/m5XbCYGabOUEEk4oCKMkAiAaLjBR/LXecxAFxzzTVYuHBhv+PtJX4MAIBVlEIs5jB1hgrGLoYzJzw3F8nEIsRr5FQzIAFFyYAMeXXVFlw4b0HqBDnUofa7hVlFGRCbAE4ivHJ7rskEDkBiaO9kcP78eZSWlvY35F44hQqIiHbMURQWLkFSmhznis1orLd6LJ8UJqd7DUhAUTIgQ5rVwnDiaCeCQ0RIm9ijWaeyDJwP/QUAUNZsRKxaBoWL6R1WrlyJZcuW+Rpu3/RJ9hrNReMnK6BUcTie0wmbre+RQklhcjR2WdHUSTOYksCgZECGtDMnu9DVyZBxhQpisb1tnbU0Aa3N9i9XH3SPJHJl5cqVeO6553yOty+cPgmoqwYzdgIAJFIO6VkqtLfxKCrouwmou3+jqL4jILERQsmADFlNBivKiswYkyqDNqJHc1CFvRmH0ycLPmaryYbadguStb07jwFg5syZuOaaa3yK1xNHvJXnHNsiY6SIT5Si+LQJrc02t2WTLiavogZKBiQwKBmQIYm3MRzP6YRCyWFCuvMaBaysCOA4n2oGRQ32Dtvx4a7XPSguLkZhYaHwgL2RmALgYvw9TJqmhFRmby5ibtY7Visk0KkkKKqjZEACg5IBGZKKC01oa+ExZboKksuGXrLSQnvnsSpI8HELDV0QcUCKm5rBU089hYcfftinmD3hQnWANgIodU42MrkIk6Yq0dxow7li930CY3UK5Ne0BiQ2Qug+AzLktLfaUJRvRIxeiug45+kiGM8DpYXgps/y6diFDUYkhsqhlLr+HbRq1SqEhob6dGxvcMnjwErP9NoelyhF5XkJTp/sQlScFKqg3vGNC1fiSEU7mrusCFXSR5f4F9UMyJDCGMPxo50QizlMnuaiKaeuCuhsB5KFLxXDM4aihi6M1blfGvOKK67AzJkzBR/baynjgMYGsCaD02aO45CepQQYcPKHTjAX8xB1N22daRA28ykh3qBkQIaU8lIzGuttmJChgELZ++3JSuxNLJwPyeBCqxkdFh7jwl03EQHAmTNnkJ+fL/jY3uKSLsZd2rtfQhUkxrgpCtRVW1FV0XuqihSdAhIRh0JKBiQAKBmQIcPYxaPgeBd0kRIkJLtZuay0EFAG+XTncfeX6Dg3nccAsHr1aqxYsULwsb2WkAJIJPZ+DxeS0uTQhIlx6lgXzCbe6TGZWISxEUE4U0/JgPgfJQMyJDDGcPKHLvA8kJGldDstNSs9AySNBScS/tY922BEkEyEWLX7JTJXr16NP/zhD4KP7S1OKgUSUtwmA5HIPlWFxcyQ72IhnEkxahQ3GmF1M+qIEF959YnKy8vDo48+il//+tf45JNPej1eUFCAVatW4Y477sC3337r9yDJyFddaUHNBQvGTVIgyM3C9szYCVwoB5fiy9Ly9prBWJ2y17TVPU2dOhVZWVk+Hd9bXPJ44HwxmNX1rKXqUDFSJ8hRec6CumrnfSbHhMBsYzRPEfE7j8mA53ls3rwZzzzzDF599VUcOnQIlZWVTvuEh4fjwQcfxJw5cwIWKBm5zGYep45dXLBmnOs7gwEAZUUA433qL+i02FDeYuqzvwAATp06hePHjws+viDJ4wCL2enms8ulTVQgKESEE0c7YbVcqgVMjg4BAOo3IH7nMRkUFxcjOjoaUVFRkEgkmDVrFnJycpz2iYyMRGJiok8rThFSkGeE2cSQcYXSPiOpG46mlSThyaDYYATP+u4vAIA1a9bgN7/5jeDjC9Fds+nuDHdFLOaQcYUKXZ0MZ05e+uKPCpFDq5SgsJ5qBsS/PA5WbmxshE6nc/yt0+lQVFTURwn39u3bh3379gEA1q9fj/DwcJ+OI5FIfC4bSBSXMBKJBMYOJSrKmpGeGYaUNF2f+zdVlsEWl4jwxDGCz1VZZv9CvWpsHNQK9+sPb9iwAWKxOKCvF9Pp0KANh6zqHDR9nCc8HGiqr8fpky0YPzkC0bFKSCQSpMdpUFjXPqSu6VB+j1Fc3hnQO1eys7ORnZ3t+LuhocGn44SHh/tcNpAoLmHUIWH45ssaBKtFiE/m+4yRMQb+zElwGVf49Fxyyw2IU8tgbm9BQ7v7/eLi4gbk9eLHjIWx4DgsHs4zJg04XyrCgb3VuOa6EERHRyBJLcJXxSYUVdQgbIjcfDZU32MjMa7Y2Fg/R2PnsZlIq9XCYLh0g4zBYIBWqw1IMGR0+f6QAUYjw7QZl2Ykdau+Gmhv9elmM8bYxc7jvvsLAPtgiaNHjwo+h1Bc8jigoRastanP/SRSDhlXKNHRzqPwpL1paBzdfEYCwGMySElJQXV1Nerq6mC1WnH48OGAj7YgI19dtQVFp1uROl6OUJ3nX7es2D6Fg083m7WZ0WK0YXxE3/0FALB27Vo8/fTTgs8hlON59NFv0C08SooxqTKUnjWhtroLKdqLN5/R/QbEjzx+CsViMZYuXYp169aB53nMnz8fer0e27dvR0pKCrKyslBcXIxXXnkFHR0d+OGHH/DPf/4Tf/7znwcifjIMmc08jud0QhMmxdhJnn+tAwBOHweCQ4DYBMHny6u2z/Q5LcbzxHZr165FWFiY4HMINiYNkMnBTueBm3aVx90npCtRW23FN/vqMCdbhRStAgX1nYGPk4waXjU4ZmZmIjMz02nb4sWLHf9PTU3FX//6V/9GRkaskz90wWRkuPbHUYCojwb8ixjPgxXkgpswFZzI9T0Ifcmr7kBMiBRRwe5vNus2fvz4AWln5qRSYNwUsPxcr/aXSDlMm6HC4f3tyM/rwtQYFXacMqDNZEOIXPhrQsjl6A5kMqAunDejqtyCsZMVCI/0slZw4bx9ZbNJmZ73vYzFxnCythNTo72b7jonJwdHjhwRfB5fcJOm2Vc+q6/xan9dpASTp4WivNSMsVIleAYcr6H1DYh/UDIgA6ark8fJH7oQphMjdXwfN5ddhuUfAwBwk6YKPmdhQxeMVuZVExEAvPTSS3j++ecFn8cX3KRpAOB17QAAMq/UQR0qgqHQBp1UjGNVlAyIf1AyIAOC8Qy533WCZwzTrlL1eXNZr7L5uUBcon1xGIFyqzsg4oAp0Sqv9l+/fj3eeOMNwefxSVQcoIsUlAzEYg7TrgyC1cKQLQvDsaoOl9NdEyIUJQMyIIpOm2Cos2LyNCWCgr1v42YmI1Bc4PgVLVRedQfGhyuhknp3ztTUVIwb59vcR0JxHGd/XmeOg1mtXpdTh4oxIUOJEJMEsSYZzjebAhglGS0oGZCAa6izojDfiLhEKfRJnjtxnRSeBKxWn5JBq9GKkkYjpnrZRAQAR44cwYEDBwSfy1fcpGmAscvl+gZ9SUqTQRslxgxRCHJLqKmI9B8lAxJQJiOP3G87EBQsQvp0leD5q1h+LiCTAWmTBJ/7eE0nGCAoGfzpT3/Ciy++KPhcPhufAYhEgpqKAHut4oqZQTCLeFjLOFjM1FRE+oeSAQmY7n4Cs4lh+szeC9t7dYyCXGDsZHBSgTUKAHk1HQiSiZCq9XLUEuzJ4K233hJ8Ll9xqiAgeZz9eQokk4tgjuMhs3E49h31HZD+oWRAAubMKSPqa6yYNE0JTZjwOXSYoQ6oueBTExFjDLnVHciIDoJYQGd1YmIikpOTBZ+vP7hJ0+zrG7S1Ci6bnqJCDt+Guioris9Q3wHxHSUDEhBVFWYUnzYhIVmGxBThv+oBgJ3qHlIq/P6CsiYTDJ1Wr4eUdjtw4AC+/PJLwefrD25SJsCYT7WDCRFKFIm70Blkw5kTRtRWu14whxBPKBkQv2tttiHv+06E6cSYnOl+CUtP2PcHgMhYn9Y7/qqsBRIRcJU+RFC51157DevXrxd8vn5JTAFCtWA53wguKhWLkB4dhH3mJoRoRMg90on2NlsAgiQjHSUD4lcmI4+cgx2QSDhkzQ7yPBupG6yhFjh7CtysBYKTiY1nOHCuFdNjg6EWOFXDhg0b8M477wgq01+cSAzuynnAqR/AWpsFl587Ro26LiuCx4oADsg52AGzmfd/oGREo2RA/MZqZfj+mw4YjTyumBMEhdL3txf79isAAHflXMFlT9R2oslow7wkteCycXFx0Ov1gsv1FzdzPmCz+VQ7mBEfjCCZCAeqW5E1W4WOdh5HD3bAZqMOZeI9SgbEL3ie4diRDjQ32TB9ZhDCvJiW2h3GGNiR/fZRROFRgst/VdaCIJkIWXHBgsvu378fu3fvFlyuv7i4RCAhxf68BZKJRbg6UY0jFW1QhYkwdYYKhnp7Ux2NMCLeomRA+o0xhlPHulBbZcWUTCWi49wvK+mV0kKgrsr+a1kgo5XHtxVtmJ0QAplY+Nt748aNeOWVVwSX8wdu5nz7qKIL5YLLLkjWwGxjOHS+DfGJMkxIV6Cq3ILTJ2itZOIdSgakXxhjKMgz4nyJGakT5BiT6v0EdG6P+e1+QCoDN3224LLfVrTBaGWYl6Tx6dxvvvkmtmzZ4lPZ/uJmXGO/Ae1b4bWDsToF4tQy/Le0BQCQMl6OMakylJwx4Ww+JQTiGSUD4jPGGM6cMKL0rAlJaTKMn+L9zV1uj2mxgH3/DbhpV4FTeje5XE9flbUiMkiCCV6sauZKZGQkoqOjfSrbX5w6FJiUCfbtV2C8sBFBHMdhQZIGBfVdqG4zg+M4TM5UQj9GhsJTRhQVUEIgfaNkQHzCGEPhKSOKz5iQmCLDpGm+DyF1cjIH6Gz3qYnI0GnB8ZoOzB2jgcjHWPbs2YPPPvvMp7L+wM1cADQbgDMnBJedl6wGB2B/mb12wHH29ZPjE6U4c9KI4tOUEIh7lAyIYIy39xEUFdhvKpsy3T+JgDEGfu+nQKgOmCB87YJ/FTQCALJTfGsiAoBNmzZhw4YNPpfvL27qDCAoBPy+fwsuG66SIiNahX0lLbDY7ENLORGHqTNUiEuQ4vQJI06f6KJOZeISJQMiiM3G8MO3nThXbEbyODnSs/xUIwCAgjz7dNU33ApOLOz+AEOnBV8UNWNBsgbRIb7d8QzYk8G2bdt8Lt9fnFQG7rqfAiePgpWcEVz+5glaGDqt2FPccumYIg7TrlQhIVmG4tMmHM/pAs9TQiDOKBkQr5lNPL470IHqCgsmZigwaar/EgFjDPzOvwPacHBzFgku/3FBI3jGcNsk4Qvg9KTVahEeHt6vY/QXN/9GIEQD/tN/CC47SHo0RAAAFahJREFULSYIkyKV2HGqASbrpRvPOBGH9Cwlxk6So6LMjJyDHbBYKCGQSygZEK+0NFnxzd52NDZYMe1KFVLG97+z2MnJo0DZWXA3LrYvFi+AodOC3UXNmN/PWgEA7Nq1C5988km/jtFfnEIJ7vqfAwV5YGfzhZXlOPwqIwJNRhv+U9jU67Fxk5WYMl2J+horDu5tQ1srTV1B7CgZEI8qz5lx8Mt28DzD7PnBiB/Tvy/cy9lrBf8AwqPAzVoouPxH+QbwjOH2yf2rFQDAO++8g40bN/b7OP3FzfsRoAkDv/Pvgtv4J0aqkBkThI8LDOgw9/6yH5Mqx1XzgmA2M3yztw3VlWZ/hU2GMUoGxC2L2b4wTe53nQjTinHNohCEhft+Z7Fbud8C5SXgfnwHOImw49e1W7C7uAULkjWICu5/knrnnXfw4Ycf9vs4/cXJ5OB+dBtw9pRPI4t+mRGBNjOPT880unw8PFKKaxaFIEQtxtFDnThxtBNWajYa1SgZEJfqaiz46os2XCi3IG2iHFfNC4Zc4f+3C2trBb9tExAdD+6qeYLK2niGVw9XQSLicPtk/7Tzq9VqaDS+j0byJ+6a6wBdJPgtG8G6OgWVTdUpMFMfgk9ON6KixfU6B0qVCLMWBCNlvBznS8z4encbDHXer8VMRhZKBsRJVyePY0c68N3XHZBIOczJDsb4KUqIBCwQ4y3G8+DfeRVob4HovpWCRxBtP9WAgvouLJ8Rhcjgfk6BcdHOnTuxY8cOvxyrvzipFKJ7HwcMdWAfvCG4uei+rEjIxSK89M0FGK2uZzEVizlMzFBi9oJggAMO729H3vedMHbRrKejDSUDAsA+4+jZfCP272pFdaW9NnDNtSEI1QagWeiizk/+Dpz6Adzie8ElpAgqe7K2AztOGbAgWe3z1BOubNmyBZs2bfLb8fqLS50I7pYlYEcPgn39uaCyOpUUj8+ORWWLGf/3XU2fyUQbIcHc60KQMl6OyvNm7N/ViuIzRpr5dBQJ3CedDAtWC0NZsQmlhSaYTQwx8VJMnKqAKkjYr3ShWHEB2v++Cdz02eDm/khQ2eYuK/58qBrRwTLcn+XfqSO2bNkCnU6Hzk5hzTKBxF33U7Czp8C2b4Zl2pWAxvuO8qkxQbgjPRzbTjRgYqQK16WFut1XIrHXEhKSZSjI68Lp40aUFpqQMl6OxBQ5JBL/1w7J0EE1g1Gqo92G08e7sO+zVpw5YYQmTIzZC4KRNTso8Ing9HHwr/0O4shocP/zsKB7FarbzFi15zzazTY8MScWSql/38JKpRIqlfA5kQKJE4kgWroCCFaj6YUVYMUFgsrfPlmHqTFB2HS0xjGRXV+CQ8SYcXUwZs4LQrBajII8I778rBVnTnahs4Oaj0Yq8Zo1a9YM1snb2tp8KqdSqYbUL7duQz0uq4WhutKCguNdyM81oslgQ0SMFNNmqJA6QQFlUOB/G/CHvgTb9DIQEQPdCxtglHl/v8LZhi48/2UFzDzDCwv0SNP5NhldXz766COcPXsWKSnCmq0CjZMrwE2dAVHe9+D3/RtcdBy42ATvynIcrogLxlmDEZ+eaYKNZ5gcpfKYhFXBYuiTZIiIkqCrk0d5qQVlRSa0NFrBiQBlkMjRlzTU3/tDTX/iCgkRtpSrt6iZaITr6uRRdLoVxYUdqKuxgLcBCiWHcZMV0CfJoFQNTOWQdXWC/Xsb2N6dwIQMiB54CuKIaKChwWNZG8+wu7gZ7x2rQ6hSgt/O1yNO7d97Hbpt27YNUqkUixYJvws60LjIWGjXv4X6F1eCf+tlcJXnwP3oVnByzwk1WCbGb+fr8X/f12BHvgEX2sy4PysKYUrPXwHaCAlmRASjs4NHeakJ5aVm1FZ1QiwGImOkiIqTQqWkUUjDHccGcdaqqqoqn8qFh4ejwYsvkYE22HExxtDRxqPJYEOTwQpDvRXtrfZqvULJISZeihi9DNpwsf/mE/IUk9UC9vUXYJ9tB9pbwV1zHbhf3A9OIvX4ejHGkHOhHe/n1qOy1YzJUSo8MTsWoV58gfnKYrEgPDwcLS2em1MGQ3h4OOqrq8A+2Ghf90CjBfeTO8DNvtar0ViMMfzrdCO25NVDKuJw03gtfjpRi2CZ902DjGcwNFhRVW5BzQULTEb7V0iIRgRdhARhOgnCdGKogkUD9j5zZ7A/k+70J67Y2Fg/R2PnVTLIy8vDu+++C57nsXDhQtxyyy1Oj1ssFrzxxhsoLS1FSEgIVqxYgcjISI8np2TgG4uFoauDR0e7DZ3tPNpbebS22NDWaoPt4g80iRQI00kQESXB/2/vbIOjKNY9/puZfUk277snJEJAIAbPhToIYSOcKAKC1C31VFlcRbFKLloWWoHIS2EppeIHRVCMoTRQ8gG4mKpbFblFinM/XEDEwOWtEhKCEFQIIHIgEpPNy8ZNyO5O3w+bLEl2QxLMbMK5/dua3emenvR/nu6Zp7tnMp3x52T8ojmCDsAHF84hTp9AnD4JTQ3w58mo//bvKGMzgunC2UsIwZWGWxz7xc3xX9zccLczMs7CkqnJPJwWG5FjGK71C7prE9Xn0f/rP+DSj5DoQMn8K0pmNmT8C4p654v7jeZ2/vP73/jfq25izCpZabHMSItj6sgYokz97y0KIWhq8ONpsXL1chMN9b5udTAuXiMuQSM2XiUmVsMWo2KLUTGZI1MXh2tZ3pPOQNd1VqxYwbvvvovD4WDt2rWsWLGCtLS0YJr9+/dz9epVli5dyrFjxygtLWXVqlV9Zv7/yRkIIRA66AJ0v0DXA79+f+BNoH4f+PwCv0/gbRf4vAKvV9B+q3PRaWsTtLXqwZOtE4tVIS5BIz5BJT5RI8lhIjb+dqtsMO0lhACfF9paodUDzY3Q5EI0uuDGL4hrV+D6VWi/BRYr/GUa6qPzYdJUFEXBpwtavToerx81Oo7LNXW4PD5q3O1cabjFlYY23O06qgJ/SbHx2NjAo6MmA/7PIRxFRUXExcXx5JNPRiS/gdKzLIUQ8H0Z+tGDUFUB3nawRkPa/ShpY+G+MShJdkiwQ3wiREVDlC34/qfLrjb++ycXZf9owd2uY1IVRidYGJtoZUyilWSbmaRoE0nRJmLMKtFmFYumhDjlTl1CF7ibdRrqfTQ3+nE3+Wlu0vG2d7/MmEwQFa1ijVaxWBWsVgWzpWMxK5jMCppJwWRS0DTQTAqaCqqmoGqgqgqqCorCHRsI9+K1oi+McgZ99rerq6tJTU0lJSUwMXl2djZlZWXdnMGpU6d47rnnAJgxYwY7duxACGFIK+5//n6ext8dwN2ObvWtKVwKpcda13DnuqLUoXRJoXR8Kyh3NdmKEAIvftqFH6/wcatjaRNeWnUvraIdj96O73cdwr91oIvmfthL3F4RXfcRHV9CdKx2xHcck0BBkAiqHTEqC3G/Gd1sRTeZ0QX4fgRv1UV8uk4v//uERVO4P9FK9ph4MhxRPJwWS0JU5G9p7d69G7PZPGydQU8URYGHHkZ76GFEWyucKw88hvqPnxGlR6DVE77kNQ1MZu7XTCw3mfCrJn6IG0NF/Hh+bhpBZe2f+M4cGzZPVeiYhR+T8GMSOprQURGoQu+o86Jj6dAowIyKTTUTrViIVs1EeU1EtZmxNpowKxoWRcPM3Q1f6kJw+wN0/ApAiN86Ynp+hwvTY0tf3P0I+6jkah6b98Bd728EfZ5tLpcLh+P2c80Oh4OLFy/2mkbTNGw2G263m/j4+G7pDh48yMGDBwHYuHHjXb0qODHeiqvFmKcDwhdtaGxoFRK3r5fBC2jXihnmIwQCHR0dgUAX/o51Hb/woxMI94ZVCSyJffXoFaW/rqAjudI1ENhfUUBRCTTFVFRNo6O5hmq2gMWCarGiWCwoHfmpqoJJCbTeTKqKWVMwaypRJpUYi0aMxURijBV7tMafYizYbRa0CLX+70RJSQkmkwmfb3jeEDWZTHc+b9JGw78GhnGFEOhNDegNdeiuOvSmhsCN/FYPelsr+LwIrzfwq+s4/X6cuhtEM1BNs0/FhRWXYqFBWPEoJlox0YqGFxUfCl5Fxa8oCEXFL+iosUpIzRVdmk9CQJuAnvOuCUBFRUVDUzSUjnVVUVEDTarAoiiE+wQbZsrt5tjt2t+1bimEr2mhsUbVyPhYy5C/Kr0nEW16zZs3j3nz5gXDd9NN+uvsdP72T9j1M5LhqysxoKvtFg3DaEbG4WovuEttcfbAMkCigVEdiyG6IsA/oy6jhon6vFNkt9upr68Phuvr67Hb7b2m8fv9eDwew56FlUgkEsng06czSE9Pp6amhtraWnw+H8ePH8fpdHZLM23aNEpKSgA4efIkkyZNGvJHyiQSiUTSf/ocJtI0jVdeeYX169ej6zpz5sxh9OjRFBUVkZ6ejtPp5PHHH6egoIDc3FxiY2NZuXJlJLRLJBKJZJDo1z2DzMxMMjMzu8U9//zzwXWLxcLq1asHV5lEIpFIIoZ8UZ1EIpFIpDOQSCQSiXQGEolEIkE6A4lEIpEwxG8tlUgkEsnw4J7sGbz99ttDLSEsUtfAkLoGznDVJnUNjOGo6550BhKJRCIZXKQzkEgkEsnQzoH8Rxg/fvxQSwiL1DUwpK6BM1y1SV0DY7jpkjeQJRKJRCKHiSQSiUQinYFEIpFIiPDkNgPhxIkT7N69m+vXr/PRRx+Rnp4e3FZcXMyhQ4dQVZWXX36ZKVOmhOxfW1vL5s2bcbvdjB8/ntzcXEymwT3c/Pz84DzOHo8Hm83Gpk2bQtItW7aMqKgoVFVF0zQ2btw4qDp68vXXX/Ptt98GZ5pbtGhRyIsGASorK9m5cye6rjN37lyeeeYZQ3UVFhZSXl6OyWQiJSWFnJwcYmJiQtJFyl59Hb/X66WgoIDLly8TFxfHypUrGTFihCFaOqmrq2PLli00NjaiKArz5s0LmYKzqqqKTz75JKhl+vTpPPvss4bqgr7LRQjBzp07OX36NFarlZycHMPHxW/cuEF+fn4wXFtby8KFC3nqqaeCcZG019atW6moqCAhIYG8vDwAWlpayM/P57fffiM5OZlVq1YRGxs6pWhJSQl79uwBYMGCBcyePdsQjb0ihinXrl0T169fF++//76orq7uFr9mzRrR3t4ubt68KZYvXy78fn/I/nl5eeLo0aNCCCG2bdsm9u/fb6jeXbt2id27d4fdlpOTI5qamgzNvytFRUVi7969d0zj9/vF8uXLxa+//iq8Xq9Ys2aNuHbtmqG6Kisrhc/nE0IIUVhYKAoLC8Omi4S9+nP8+/btE9u2bRNCCHH06FHx2WefGapJCCFcLpe4dOmSEEIIj8cj3njjjRBd586dExs2bDBcS0/6Kpfy8nKxfv16oeu6+Omnn8TatWsjqC5Qpq+++qqora3tFh9Je1VVVYlLly6J1atXB+MKCwtFcXGxEEKI4uLisPXe7XaLZcuWCbfb3W09kgzbYaK0tLSw07uVlZWRnZ2N2WxmxIgRpKamUl1d3S2NEIKqqipmzJgBwOzZsykrKzNMqxCCEydO8MgjjxiWx2BTXV1NamoqKSkpmEwmsrOzDbURwEMPPYSmaQBMmDABl8tlaH53oj/Hf+rUqWDrbMaMGZw7dw5h8PMWSUlJwdZ0dHQ0o0aNGlI7DYRTp07x2GOPoSgKEyZM4Pfff6ehoSFi+Z89e5bU1FSSk5MjlmdPJk6cGNLqLysrY9asWQDMmjUr7HlWWVnJ5MmTiY2NJTY2lsmTJ1NZWRkRzZ0M22Gi3nC5XGRkZATDdrs95GRxu93YbLbghSdcmsHkhx9+ICEhgfvuu6/XNOvXrwfgiSee6DYPtFHs37+fI0eOMH78eBYvXhxSQV0uFw6HIxh2OBxcvHjRcF2dHDp0iOzs7F63G22v/hx/1zSapmGz2XC73cHhN6Opra3lypUrPPDAAyHbLly4wJtvvklSUhIvvfQSo0ePjoimO5WLy+XqNsm7w+HA5XKRlJQUEW3Hjh3rtUE2VPYCaGpqCtogMTGRpqamkDQ966PR16xwDKkz+OCDD2hsbAyJf+GFF8jKyhoCRaH0R+OdKmHn37Db7TQ1NfHhhx8ycuRIJk6caJiu+fPnB8dEi4qK+Oqrr8jJyflD+Q2Grk577dmzB03TmDlzZq9/Y7Dtda/R1tZGXl4eS5YswWazdds2btw4tm7dSlRUFBUVFWzatInPP//ccE3DuVx8Ph/l5eW8+OKLIduGyl7hUBRl2E4JPKTO4L333hvwPna7nfr6+mDY5XJht9u7pYmLi8Pj8eD3+9E0LWyawdLo9/spLS29403OzrwTEhLIysqiurr6D59E/bXd3Llz+fjjj8Nq6mrH+vr6u7bRQHSVlJRQXl7OunXrej0pjLBXuDz6Ov7ONA6HA7/fj8fjIS4ublB1hMPn85GXl8fMmTOZPn16yPauziEzM5Pt27fT3NxseI+lr3Kx2+3U1dUFw4NVp/rD6dOnGTduHImJiSHbhspenSQkJNDQ0EBSUhINDQ1h87Xb7Zw/fz4YdrlcEXe0w/aeQW84nU6OHz+O1+ultraWmpqakG60oihMmjSJkydPAoELkNPpNETP2bNnGTlyZLcuXlfa2tpobW0Nrn///feMGTPGEC2ddB2nLS0tDdslTk9Pp6amhtraWnw+H8ePHzfMRp1UVlayd+9e3nrrLaxWa9g0kbJXf45/2rRplJSUAHDy5EkmTZpkeKtOCMGXX37JqFGjePrpp8OmaWxsDN67qK6uRtd1w51Uf8rF6XRy5MgRhBBcuHABm802LIaIhsJeXXE6nRw+fBiAw4cPhx31mDJlCmfOnKGlpYWWlhbOnDkT9ilJIxm2/4FcWlrKjh07aG5uJiYmhrFjx/LOO+8AgWGG7777DlVVWbJkCVOnTgVgw4YNvPbaa9jtdm7evMnmzZtpaWlh3Lhx5ObmYjabB13nli1byMjIYP78+cE4l8vFtm3bWLt2LTdv3uTTTz8FAr2IRx99lAULFgy6jq588cUX/PzzzyiKQnJyMkuXLiUpKambLoCKigp27dqFruvMmTPHcF25ubn4fL7g/YuMjAyWLl06ZPYKd/xFRUWkp6fjdDppb2+noKCAK1euEBsby8qVK0lJSTFESyc//vgj69atY8yYMUHHs2jRomCLe/78+ezbt48DBw6gaRoWi4XFixfz4IMPGqqrt3I5cOBAUJcQgu3bt3PmzBksFgs5OTndHgk3ira2NnJycigoKAj2ArrqiqS9Nm/ezPnz53G73SQkJLBw4UKysrLIz8+nrq6u26Olly5d4ptvvuH1118HAvfRiouLgcCjpXPmzDFEY28MW2cgkUgkkshxzw0TSSQSiWTwkc5AIpFIJNIZSCQSiUQ6A4lEIpEgnYFEIpFIkM5AIpFIJEhnIJFIJBLg/wC5G/6tRd6oOAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XNu-1aQC3hfJ"
      },
      "source": [
        "With continuous distributions, we do not want to find the probability of a random variable at any given value. Since the range is infinite, the probability that a continuous random variable takes on any given value is zero. \n",
        "\n",
        "We are usually interested in finding out the probability that the random variable lies between two values. \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WSSklC1x3hfJ"
      },
      "source": [
        "#### Programmatic solutions: percent point function\n",
        "\n",
        "Recall the definition of the **cumulative density function**: \n",
        "\n",
        "$$F(x)=P(X\\leq x)$$\n",
        "\n",
        "The CDF returns the probability that a random variable is less than $x$. For instance, because of the symmetric shape of the normal distribution, the CDF of the standard normal distribution at 0 is expected to be 0.5. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w-h-D9zX3hfK",
        "outputId": "29cd16fb-937d-4bad-ce92-7af0441d1cea"
      },
      "source": [
        "norm.cdf(0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6wD5AryX3hfK"
      },
      "source": [
        "We will also use the **percent point function**, available via the `ppf()` method. The percent point function does the inverse of the cumulative density function. It returns the percent point given the value of the CDF: "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VujTl2v53hfL",
        "outputId": "ddaaa577-ffe0-41b8-fe7b-928d670d96a5"
      },
      "source": [
        "norm.ppf(0.5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LROjzD_Y3hfL"
      },
      "source": [
        "#### Standard deviation rule/empirical rule \n",
        "\n",
        "A useful rule of thumb is the **standard deviation rule**, or empirical rule. \n",
        "\n",
        "This rule states that for a normally distributed random variable, \n",
        "- 68% of data lies within 1 standard deviation of the mean.\n",
        "- 95% of data lies within 2 standard deviations of the mean, and \n",
        "- 99.7% of data lies within 3 standard deviations of the mean."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zqkERi0j3hfL"
      },
      "source": [
        "#### Example: height\n",
        "\n",
        "Maalysian males' heights are normally distributed with mean 169.57 and standard deviation 7.57. Answer the following questions programmatically and using the empirical rule. \n",
        "\n",
        "- 84% of Malaysians have height of less than ... cm. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rEsdL9F23hfM",
        "outputId": "2815b8de-f0d6-48b1-b7f6-11d927234e33"
      },
      "source": [
        "norm.ppf(0.84, loc=169.57, scale=7.57)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "177.09804617589782"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WkfIQtqZ3hfM",
        "outputId": "2cd432c4-6f2d-4b62-9cf7-8ab30810b4e8"
      },
      "source": [
        "169.57 + 7.57"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "177.14"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DNI6ceoC3hfM"
      },
      "source": [
        "- The tallest 2.5% of Malaysians are taller than ... cm "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lWSgKwPl3hfN",
        "outputId": "e745c332-8422-404c-8cb0-989eb24fe6b0"
      },
      "source": [
        "norm.ppf(0.975, loc=169.57, scale=7.57)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "184.4069273629682"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "grKpUsPA3hfN",
        "outputId": "3e08e3bf-606d-493a-a33e-7aa160886f0d"
      },
      "source": [
        "169.57 + 2 * 7.57"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "184.70999999999998"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PuheWpm43hfN"
      },
      "source": [
        "- The shortest 0.15% of Malaysians are shorter than ... cm"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OdyrBlxA3hfN",
        "outputId": "14222177-dea4-44b5-f6e4-66f32bd52da2"
      },
      "source": [
        "norm.ppf(0.0015, loc=169.57, scale=7.57)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "147.10422390516268"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UNE-qNXj3hfO",
        "outputId": "1e56885b-8c57-4b52-b5cf-0ca759b448bf"
      },
      "source": [
        "169.57 - 3 * 7.57"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "146.85999999999999"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8XpK4xAZ3hfO"
      },
      "source": [
        "### Poisson distribution\n",
        "\n",
        "The Poisson distribution models the number of events that occur in a fixed time interval. \n",
        "\n",
        "Use the Poisson distribution when: \n",
        "- events occur at random points of time and space, and\n",
        "- our interest lies is the number of occurrences of the event.\n",
        "\n",
        "The most important property of the Poisson variable is that the waiting time between events is **memoryless**: \n",
        "- the time when events occur do not affect the number of successes in an interval;  \n",
        "- only the length of time affects the number of successes.\n",
        "\n",
        "The Poisson distribution has a single parameter: lambda ($\\lambda$). The mean and variance of the Poisson distribution coincides with the shape parameter $\\lambda$. \n",
        "\n",
        "The probability mass function of the Poisson distribution is as follows:\n",
        "\n",
        "$$p(X=k) = \\frac{e^{-\\lambda}\\lambda^{k}}{k!}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c1N3SE493hfO"
      },
      "source": [
        "from scipy.stats import poisson"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "fJi3i-bw3hfO",
        "outputId": "094574c2-49af-4d42-ceb9-a7efe8184571"
      },
      "source": [
        "# a Poisson distribution with lambda=1 can be interpreted as: \n",
        "# on average, 1 event occurs within the set time interval. \n",
        "# naturally, it is less likely that more than 1 event occurs. \n",
        "\n",
        "x = np.arange(10)\n",
        "f1 = poisson.pmf(x, mu=1)\n",
        "f2 = poisson.pmf(x, mu=2)\n",
        "f3 = poisson.pmf(x, mu=3)\n",
        "\n",
        "plt.bar(x, f1, label=\"$\\lambda=1$\")\n",
        "plt.legend()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fad829e4d10>"
            ]
          },
          "metadata": {},
          "execution_count": 22
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ODe9dJJQ3hfP",
        "outputId": "a3a0f5b0-8ac7-43e4-e824-ef2ad88aa184"
      },
      "source": [
        "# the average can be calculated by multiplying the inputs with the values of the PMF\n",
        "x @ f1\n",
        "# see that this is equal to lambda "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.999998874797402"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "3BKXdO313hfQ",
        "outputId": "27e80d49-d5a5-499d-94a5-4aede33a90e6"
      },
      "source": [
        "# for lambda=2, having 2 events is a lot more likely\n",
        "\n",
        "plt.bar(x, f2, label=\"$\\lambda=2$\")\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fad82947d50>"
            ]
          },
          "metadata": {},
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "amQSbmPL3hfQ",
        "outputId": "01449eee-7cb9-45b8-f728-351f8738b9c7"
      },
      "source": [
        "x @ f2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.9995251053434773"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "mcvzOTrw3hfQ",
        "outputId": "7e0e9f55-5964-454a-9b2f-0ba347fb7010"
      },
      "source": [
        "plt.bar(x, f3, label=\"$\\lambda=3$\")\n",
        "plt.legend()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fad828cebd0>"
            ]
          },
          "metadata": {},
          "execution_count": 26
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD4CAYAAADiry33AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAPxUlEQVR4nO3df6zddX3H8edrbaFTjCDUP9YCt0bGVimDUambgcSBWFMCM6laE7UuLM0MTPcr47otMKsxuJFt/gEbRFhE3TqHZrkZBVaHS4gLrAWKtLDGSy1wOxZrC0oYLW157497ai6Xi/e098dpP+f5SG445/vjfN/fAM+efs+Pm6pCktSun+v1AJKkmWXoJalxhl6SGmfoJalxhl6SGje31wOMd9ppp9XAwECvx5Ck48pDDz30o6paMNG6Yy70AwMDbN68uddjSNJxJclTr7fOSzeS1DhDL0mNM/SS1Lhj7hq9JHXrwIEDjIyMsG/fvl6PMmvmz5/PokWLmDdvXtf7GHpJx62RkRHe9KY3MTAwQJJejzPjqoo9e/YwMjLC4sWLu97PSzeSjlv79u3j1FNP7YvIAyTh1FNPPeK/wRh6Sce1fon8YUdzvoZekhpn6CWpcb4Y24iBwbtm/Bg7b1h5zB1b0uQMvaRmTPeTjm6fYDz22GNcfvnlDA4O8slPfvKojrVv3z4uvvhi9u/fz8GDB1m1ahWf/exnj+qxxvPSjSRN0dKlS1m/fj133HHHUT/GiSeeyH333cejjz7Kli1buOeee3jggQemZT5DL0nT4K1vfSvbtm076v2TcNJJJwGjHwQ7cODAtL2jyEs3kjQNBgcH2b9/P0899RRnnnnmq9ZddNFFvPDCC6/Z58Ybb+TSSy/96f1Dhw5xwQUXMDw8zNVXX83y5cunZTZDL0lTdPfdd/Piiy+ycuVKtm3b9prQ33///V09zpw5c9iyZQvPP/88H/jAB9i6dSvnnHPOlOfz0o0kTcG+ffu49tprufnmm1m6dClbt259zTYXXXQR55133mt+vv3tb0/4mCeffDLvec97uOeee6ZlRp/RS9IUfP7zn+fjH/84AwMDLF26lKGhodds080z+t27dzNv3jxOPvlkXnrpJTZu3Mi11147LTMaeknNmO3PW2zfvp2NGzfy3e9+Fxh9980XvvCFo3qsZ599ljVr1nDo0CFeeeUVPvShD3H55ZdPy5yGXpKO0tlnn82DDz74qvsPP/zwUT3WueeeyyOPPDJdo72K1+glqXGGXpIaZ+glHdeqqtcjzKqjOV9DL+m4NX/+fPbs2dM3sT/8G6bmz59/RPv5Yqyk49aiRYsYGRlh9+7dvR5l1hz+nbFHwtBLOm7NmzfviH53ar/y0o0kNc7QS1LjDL0kNa6r0CdZkWR7kuEkgxOs/4Mkjyf5XpJ/T3LmmHVrkny/87NmOoeXJE1u0tAnmQPcBLwfWAJ8JMmScZs9AiyrqnOBO4G/6Oz7FuB6YDlwIXB9klOmb3xJ0mS6eUZ/ITBcVTuq6mVgPXDl2A2q6jtV9X+duw8Ah9/78z5gY1XtrarngI3AiukZXZLUjW5CvxB4Zsz9kc6y13MVcPeR7JtkbZLNSTb30/thJWk2TOuLsUk+CiwD/vJI9quqW6tqWVUtW7BgwXSOJEl9r5vQ7wJOH3N/UWfZqyS5FPhT4Iqq2n8k+0qSZk43od8EnJVkcZITgNXAq36FSpLzgVsYjfwPx6y6F7gsySmdF2Ev6yyTJM2SSb8CoaoOJrmG0UDPAW6vqm1J1gGbq2qI0Us1JwH/nATg6aq6oqr2Jvkco39YAKyrqr0zciaSpAl19V03VbUB2DBu2XVjbl/6M/a9Hbj9aAeUJE2Nn4yVpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMbN7fUA0lQMDN4148fYecPKGT+GNJN8Ri9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9Jjesq9ElWJNmeZDjJ4ATrL07ycJKDSVaNW3coyZbOz9B0DS5J6s6kX1OcZA5wE/BeYATYlGSoqh4fs9nTwCeAP5rgIV6qqvOmYVZJ0lHo5vvoLwSGq2oHQJL1wJXAT0NfVTs7616ZgRklSVPQzaWbhcAzY+6PdJZ1a36SzUkeSPKbE22QZG1nm827d+8+goeWJE1mNn7D1JlVtSvJ24D7kjxWVU+O3aCqbgVuBVi2bFnNwkwzwt92JOlY1M0z+l3A6WPuL+os60pV7er8cwfwH8D5RzCfJGmKugn9JuCsJIuTnACsBrp690ySU5Kc2Ll9GvBuxlzblyTNvElDX1UHgWuAe4EngG9U1bYk65JcAZDknUlGgA8CtyTZ1tn9l4HNSR4FvgPcMO7dOpKkGdbVNfqq2gBsGLfsujG3NzF6SWf8fv8JLJ3ijJKkKfCTsZLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUuK5Cn2RFku1JhpMMTrD+4iQPJzmYZNW4dWuSfL/zs2a6BpckdWfS0CeZA9wEvB9YAnwkyZJxmz0NfAL4h3H7vgW4HlgOXAhcn+SUqY8tSepWN8/oLwSGq2pHVb0MrAeuHLtBVe2squ8Br4zb933AxqraW1XPARuBFdMwtySpS3O72GYh8MyY+yOMPkPvxkT7Lhy/UZK1wFqAM844o8uHlnprYPCuGT/GzhtWzvgx1L5j4sXYqrq1qpZV1bIFCxb0ehxJako3od8FnD7m/qLOsm5MZV9J0jToJvSbgLOSLE5yArAaGOry8e8FLktySudF2Ms6yyRJs2TS0FfVQeAaRgP9BPCNqtqWZF2SKwCSvDPJCPBB4JYk2zr77gU+x+gfFpuAdZ1lkqRZ0s2LsVTVBmDDuGXXjbm9idHLMhPteztw+xRmlCRNwTHxYqwkaeYYeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMYZeklqnKGXpMZ1FfokK5JsTzKcZHCC9Scm+afO+geTDHSWDyR5KcmWzs/fTe/4kqTJzJ1sgyRzgJuA9wIjwKYkQ1X1+JjNrgKeq6q3J1kNfBH4cGfdk1V13jTPLUnqUjfP6C8EhqtqR1W9DKwHrhy3zZXAVzq37wQuSZLpG1OSdLQmfUYPLASeGXN/BFj+ettU1cEkPwZO7axbnOQR4CfAn1XV/VMbWdLA4F0zfoydN6yc8WNodnQT+ql4FjijqvYkuQD4lyTvqKqfjN0oyVpgLcAZZ5wxpQP6P4AkvVo3l252AaePub+os2zCbZLMBd4M7Kmq/VW1B6CqHgKeBH5x/AGq6taqWlZVyxYsWHDkZyFJel3dhH4TcFaSxUlOAFYDQ+O2GQLWdG6vAu6rqkqyoPNiLkneBpwF7Jie0SVJ3Zj00k3nmvs1wL3AHOD2qtqWZB2wuaqGgNuAryYZBvYy+ocBwMXAuiQHgFeA36mqvTNxIpKkiXV1jb6qNgAbxi27bsztfcAHJ9jvm8A3pzijJGkK/GSsJDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDXO0EtS4wy9JDVubq8HkHR8GRi8a8aPsfOGlTN+jH7iM3pJapyhl6TGGXpJapyhl6TGGXpJapyhl6TGGXpJapyhl6TGGXpJapyhl6TGGXpJapzfdSPpuOH37Bwdn9FLUuMMvSQ1ztBLUuMMvSQ1rqsXY5OsAL4EzAG+XFU3jFt/InAHcAGwB/hwVe3srPsMcBVwCPhUVd07bdNL0iw5nl8InvQZfZI5wE3A+4ElwEeSLBm32VXAc1X1duCvgS929l0CrAbeAawAbu48niRplnRz6eZCYLiqdlTVy8B64Mpx21wJfKVz+07gkiTpLF9fVfur6gfAcOfxJEmzJFX1szdIVgErquq3O/c/BiyvqmvGbLO1s81I5/6TwHLgz4EHquprneW3AXdX1Z3jjrEWWNu5ezawfeqn1rXTgB/N4vGOFZ53f+nX84b+Ofczq2rBRCuOiQ9MVdWtwK29OHaSzVW1rBfH7iXPu7/063lDf5/7Yd1cutkFnD7m/qLOsgm3STIXeDOjL8p2s68kaQZ1E/pNwFlJFic5gdEXV4fGbTMErOncXgXcV6PXhIaA1UlOTLIYOAv4r+kZXZLUjUkv3VTVwSTXAPcy+vbK26tqW5J1wOaqGgJuA76aZBjYy+gfBnS2+wbwOHAQuLqqDs3QuRytnlwyOgZ43v2lX88b+vvcgS5ejJUkHd/8ZKwkNc7QS1Lj+jr0SVYk2Z5kOMlgr+eZDUlOT/KdJI8n2Zbk072eaTYlmZPkkST/2utZZkuSk5PcmeS/kzyR5Nd6PdNsSPL7nf/Gtyb5xyTzez1Tr/Rt6Lv8aocWHQT+sKqWAO8Cru6T8z7s08ATvR5iln0JuKeqfgn4Ffrg/JMsBD4FLKuqcxh9I8nq3k7VO30berr7aofmVNWzVfVw5/YLjP5Pv7C3U82OJIuAlcCXez3LbEnyZuBiRt8ZR1W9XFXP93aqWTMX+PnOZ3veAPxPj+fpmX4O/ULgmTH3R+iT4B2WZAA4H3iwt5PMmr8B/hh4pdeDzKLFwG7g7zuXrL6c5I29HmqmVdUu4EbgaeBZ4MdV9W+9nap3+jn0fS3JScA3gd+rqp/0ep6ZluRy4IdV9VCvZ5llc4FfBf62qs4HXgSafz0qySmM/g19MfALwBuTfLS3U/VOP4e+b7+eIck8RiP/9ar6Vq/nmSXvBq5IspPRy3S/keRrvR1pVowAI1V1+G9tdzIa/tZdCvygqnZX1QHgW8Cv93imnunn0Hfz1Q7N6Xx99G3AE1X1V72eZ7ZU1WeqalFVDTD67/q+qmr+GV5V/S/wTJKzO4suYfST6q17GnhXkjd0/pu/hD54Efr1HBPfXtkLr/fVDj0eaza8G/gY8FiSLZ1lf1JVG3o4k2bW7wJf7zyh2QH8Vo/nmXFV9WCSO4GHGX2n2SP08Vch+BUIktS4fr50I0l9wdBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ17v8Bar43pw8AdjIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9DlrYoRx3hfQ",
        "outputId": "d482333e-4ca3-48d7-d335-aa8f19650894"
      },
      "source": [
        "x @ f3"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.9885910238149727"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VqYDrtm33hfQ"
      },
      "source": [
        "**Example**: Suppose emergency calls per hour follow a Poisson distribution and occur at a rate of 5 calls per hour. What is the probability of receiving 3 calls in any given hour? "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FVRaGYAS3hfQ",
        "outputId": "7c6924be-96e7-4445-dcbe-db76e029cecc"
      },
      "source": [
        "poisson.pmf(3, 5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.1403738958142805"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hi2-slMK3hfR"
      },
      "source": [
        "## Central Limit Theorem\n",
        "\n",
        "The Central Limit Theorem helps us reason about realisations of sample means. \n",
        "\n",
        "Specifically, it tells us that in many repeated samples, the distribution of the sample means of a random variable is normal regardless of the underlying population distribution. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RcCPOfXG3hfS"
      },
      "source": [
        "from scipy.stats import poisson"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "4yyI2kzr3hfS",
        "outputId": "53220c5f-3f4b-49b7-c5a8-4b9a74e375fc"
      },
      "source": [
        "bins = np.arange(0, 40)\n",
        "p_pois = poisson.pmf(bins, mu=3)\n",
        "plt.plot(bins, p_pois)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fad827fc290>]"
            ]
          },
          "metadata": {},
          "execution_count": 30
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "goSW7f8K3hfS",
        "outputId": "a874ceb5-c77c-417a-c3a1-7d6c50a4df3a"
      },
      "source": [
        "def sample_pois(_): \n",
        "    samples = poisson.rvs(mu=3, size=20)\n",
        "    return np.mean(samples)\n",
        "\n",
        "means = list(map(sample_pois, np.arange(400)))\n",
        "plt.hist(means)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([12., 36., 39., 69., 87., 73., 40., 28., 11.,  5.]),\n",
              " array([2.05 , 2.255, 2.46 , 2.665, 2.87 , 3.075, 3.28 , 3.485, 3.69 ,\n",
              "        3.895, 4.1  ]),\n",
              " <a list of 10 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K68PVQCi3hfT"
      },
      "source": [
        "# Using Normal Distribution in Weight Initialization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TXumweFM3hfT"
      },
      "source": [
        "**Normal Distribution** could be very helpful when it comes to weight initialization of deep learning task.\n",
        "\n",
        "In deep neural network, we may encounter vanishing/exploding gradients when the derivaties become very small or very big. The activations and derivatives will be decreased/increased exponentially as a function of number of layers. This will make training difficult, especially when gradients are exponentially smaller, then gradient descent wiill take tiny little steps. Consequently it will take a long time for gradient descent to learn anything.\n",
        "\n",
        "Therefore, using a normal distributed weight initiallization with mean equals to 0 and a standard deviation of 1 could be helpful in resolving the issue."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XjIU74td3hfT"
      },
      "source": [
        "For example, when we using ReLU as our activation function, we would do the following steps:\n",
        "\n",
        "- Generate random sample of weights from a Normal Distribution having mean equals 0 and a standard deviation of 1.\n",
        "- Multiply the sample with $\\sqrt{(\\frac{2}{n_i})}$, where $n_i$ is number of input units for that layer."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OQv5WEhl3hfT"
      },
      "source": [
        "```np.random.rand(shape) * np.sqrt(2/n[l-1])```, where `l` is the total number of input units."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tz1AvTG63hfU"
      },
      "source": [
        "> This initialization is also called **Xavier Initialization**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aSLuqZXI3hfU"
      },
      "source": [
        "This sort of initialization helps to set the weight matrix neither too bigger than 1, nor too smaller than 1. Thus it doesn’t explode or vanish gradients respectively."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "id": "UbzS_wZKfvuI",
        "outputId": "ece1ed7a-df9e-43e7-8f24-be67e0f81d18"
      },
      "source": [
        "import seaborn as sns\n",
        "plt.figure(figsize=(20, 10))\n",
        "x = np.random.normal(size=(50000))\n",
        "sns.histplot(x, kde=True)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 1440x720 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TMSdlV5kkHtH"
      },
      "source": [
        "# Entropy (Optional)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-HVaNNXdkVEd"
      },
      "source": [
        "Now we define a quantity called entropy, which essentially means how much information is conveyed by probability."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nwy5Jf2EmSdH"
      },
      "source": [
        "## A solid-liquid-gas example"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WTfgwy7Elgbj"
      },
      "source": [
        "When no probability is involved, i.e. everything is known before hand, no information is gained from the experiment. All the results of the experiment could be predetermined. Look at the images below, which represent the molecules of a solid, which have low to no entropy (perfectly ordered crystal)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "id": "YLrPgp49kcKp",
        "outputId": "3d828339-ca26-4836-d295-d207c96c03e2"
      },
      "source": [
        "fix, axs = plt.subplots(1, 3, figsize=(20, 5))\n",
        "\n",
        "for ax in axs:\n",
        "    x, y = np.meshgrid(np.arange(10), np.arange(10))\n",
        "    ax.scatter(x.ravel(), y.ravel())\n",
        "    ax.set_xlim(-0.5, 9.5)\n",
        "    ax.set_ylim(-0.5, 9.5)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1440x360 with 3 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xgNFipnRlxZL"
      },
      "source": [
        "Now that we have probability in the game, we can visualize the same for say gases, when we draw the samples from a probability distribution that is uniform, a lot of information is conveyed."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "id": "trQIg3lTlRHG",
        "outputId": "bc09f104-a0ad-4fd6-a08b-3907790ec697"
      },
      "source": [
        "fix, axs = plt.subplots(1, 3, figsize=(20, 5))\n",
        "\n",
        "for ax in axs:\n",
        "    x, y = np.random.random(100) * 9, np.random.random(100) * 9\n",
        "    ax.scatter(x.ravel(), y.ravel())\n",
        "    ax.set_xlim(-0.5, 9.5)\n",
        "    ax.set_ylim(-0.5, 9.5)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PcIWM5I7juHmBDFAFhyZYuNtncbJmdnJCOvB682M6aSo/OhkLHBk/bHluTVrcgwAAJENyB0DwqIJDU44s3IOS8phOmsqPTsYCF8YP255bkwr3IAAAiZDcAQBRBYd4RSzcXa2oMCXtMZ20lR+djAXWjx8OP7fGheQZAAA2ILkDGMBiDnBHngt3pysqDEl9TIfKD+efW2N98gwwIIu5JPNRwC8kd4CCsZgDcJ7DFRXGpEzWUPnBc2sA32Qxl2Q+Cvinx3QDgOC0WswBCIrrFRUm9AwOq7Rlh0qj66Vrr9Pyz31RpTaLkZ7BYfXc9YB6v/OIeu56ILyFy4ZNtQRYo8CqlwCvZDGXZD4KeIfKHaBgLOYA1FFR0ZnGYzorKxVNT08bbpHdqF4C/JLFXJL5KOAfkjtAwVjMATiP58GgIDy3BvBHFnNJ5qNAZ2x+VlWwyR2bPxR4jsUcgA9RUQEASC2LuSTzUSA1259VFWRyx/YPBX5jMQegERUVAFAs1zd5s5hLMh8FOmD5izCCTO7Y/qEgO7YG79AXc7Z+LgAAwG++bPLGzSUXz6/mNt8vlftS/R0AmrP9WVVBJnds/1CQDV+Ct2/4XAAAgDGebvLGza9OvPO2om//HfMrICO2P6sqyFehN+t8Wz4UZIRXPNqJzwUAABhiepM3OjalaM+45h97SNGe8Vq1TRZi5lfzR95jfgVkacOm2rOpGln0rKogK3d4gNhSPh6TMR28EY/PBQAAmGJy5z3P6mXmV0D+bH9WVZDJHds/lKL5ekzG9rK5UPG5AAAAY0xu8uZ4JIz5FWzmUyGBzc+qCjK5I9n9oRTO07PHVGhZis8FAAAYYnKTN9fqmpj5Ve/QWkXMr2CYr4UENgo2uYMLfC3jzDt4J8lA+5SlzgqVcwAAwCRTm7x5VtfEza9Wbb5fJ1q8LQsohK+FBBYiuQOvyzjzCt5JMtChZqmTJLSonAMAdCMu1qhSafr/fI67cEjO1cuL51flSkWans7k7wY65WshgY1I7oBjMp1IkoEOMEsdakILQNhIJhSrWayZ27Fb0fszxCFYi+plhMjnQgLbkNwBgaYDSTLQQWapA0xoAQgbSW0DmsSa088/LZ09SxyC1aheRnAoJChMouTO6dOn9dRTT+ndd99VqVTSPffco4997GN5tw0tZL1LSKBJJ0kGOsQsdZAJLUjyO07EHv+QSIijhqR24ZrFlPmZaVXPnUv1MyiOz3ECQHMUEhQnUXLnmWee0Q033KAHHnhAc3NzOnv2bN7tQgvsElogSQY6wCx1iAkt1PgaJ2LH2zffkEolaebYha8xBnspyUYKSe3iNYs1vf0VzZ09SxyylK9xAkB7FBIUo21y589//rMOHDigb37zm7UfKJdVLnOayyh2CbuSRdVTkgx0kFnqABNacC9OpBoD4sbb92MeTskY7J2kGykktQ1oEmtWbLxbZ9+fKTQO8bylZFyLEwDgoraj6tGjR3XppZfqhz/8of7whz9o3bp12rx5s5YvX15E+xCDXcLOZVn1lCQDHVqWOsiEFpyKE2nHgDTjKmOwZ5JupJDULlyzWFMeHlFPua+wOEQldXIuxQkAcFXb5M78/LwOHjyoO++8U9dcc42eeeYZvfjii/qbv/mbBd+3d+9e7d27V5K0c+dOVT58HWVHjSqXu/p5XzTrh5NDazQ7ObHk68uH1mhlTv02N3VIp59/WvMz0+rtr2jFxrtVHh7J5Xc1yvpaOPncbs3GTNaXvfSCVm7ZntnvyZpT90SlIn3i0Vz+aqf6ISBJ4kSWMULq/FpIOwY0G2/j9Lx/TKvmPihkbKzjnsivD2ZOn1Lc01vKp0+pv/H3VSqa27HbSIxc0K7QroWYWHO+D3KMQ41cnVOY4FKc8Al9UEM/1NT7wdS6zga+XwttkzsDAwMaGBjQNddcI0m6+eab9eKLLy75vrGxMY2NjZ3/8/R0TNl6QpVKpauf90WzfohuvU068PqSXcKzt96WS78t3pk6J2n2wOsqFbAzlfW1MH/kcOzXZ48c1jmLr7lQ74nF5e79m+/XiXKf6WZ1ZWTEv+CZJE5kGSOkzu+JtGNA7Hi7urLgmTvnv/folI5vu6+QsbEu1LGhUV59EK24JPbrcysuWfr7yn3SHffVfk7SCUkq+HPhWii+D/KaUxAnakzFCZ/QBzX0Q02lUtHRA78ztq6zgS/XQrM40dPuB1etWqWBgQEdOnRIkjQxMaHLL78829YhlZ7BYZW27FBpdL107XUqja7P94ZsVZrumGbPQODZCPapJxWr+/dJkxOq7t+nE9u/XUv4wCouxYm0Y0DsePvgP6r0nUekgcuW/oCjYyOWqv7VF6Vli46McNwKDZhTJOdSnIAZ0bEpRXvGNf/YQ4r2jDPfy4tH6zoslehJZnfeeaeeeOIJzc3N6bLLLtO9996bd7vQRpHPcvHqGT88G8EdMcFn/sh7KvHQWis5Eyc6GAOajbfzlSHp+NElX3dybMQC0bEp6f/+QDo7e+GLy5ZLf3t/EDubaC86NqXq7Bmp/BFpruEAH3OKppyJEygcz68qjlfrOiyRKLlz1VVXaefOnXm3BZby6U0gPPDXHQQft5iME2neVpPlGODT2IhF4nY2z86q9B//Ln38OjNtgjUWL0QlSR/5iPTJv1Tp63cxp2iC9QSa4k3AhWHu4reg3kFY5OsqvXo1pmfVLqG9wcpVBB8k0cluX2ZjgGdjIy4guYyW4hai586ptPwid+d6gEGMuQVi7uK1YJI7RZb7+VZaSLULjIgJPr1DaxURfNDI4G4fY6O/SC6jFRaiQLYYc4vD3MVvwSR3Cl0AeFhaSLUL8tCqwi0u+Kzy4G1ZyJbpRVZIY6NXFantsLOJFliIIitBjautMOYWKqS5S2iCSe4UuQAwvdgA8pLlJCRJhdvi4FOuVAp/vTDsxiKrGL5VpLbDziZaYiGKDIQ2rrbCmAtkI5jkTtIFQBaLVxYb8FHmkxAPK9xgAIusYgR4v7KziWZYiCITAY6rrTDmAt0LJrmTZAGQ2eKVxUZLlKA6KuNJCBVuyAKLrGJwvwILsRBFtxhXAWQtmOROogVARotXFhvNUYLqrqwnIVS4ISsssvLH/QoA2WJcBZC1YJI7UvsFQJaLVxYbTVCC6qzMJyFUuAHu4H4FgGwxrgLIWFDJnXbIoOePElSHZTwJocINcAf3q92iY1M6+dxuzR85zGdjAMfN0QnGVQBZI7nTiAx67kiguSuPSQgVboA7uF/tVD/uPMtxZyM4bo5uMK4CyBLJnQZk0AtAAi2WK7t+TEIAwDIcdzaL/gcAWILkziIsXvNFAm0pdv0AAJ3iuLNZ9D8AwBYkd1A4EmiLsOsHAOgQx53Nov8BALYguQMYxq4fgCK5cgwUCXHc2Sz6HwBgCZI7gGHs+gH28TUBwjFQ/9SPOy976QXN8ras3MWNDSWOmwMALEByBzDN8K6fr4tYoFNeJ0A4BuqlnsFhrdyyXeemp003xWvNxobSlh3q4f4BABjWY7oBQOh6BodV2rJDpdH10rXXqTS6vjZRLGARWZ+oVvfvkyYnVN2/T9Vd22oJHyBUrRIgjuMYKNAFj8cGAID7qNwBCtCuOsbYQ6bZxQeW8DkBwjFQoHM+jw2A76hUtwOfQ75I7gA56+aIR30AnDl9StGKSzIfAJmoAkt5nQDh4a9IiAn4Ul6PDTCK+y1fc1OH/D1u7RCvj71bgmNZQN46LONuPDJ17ne/yeXIVLMJKRNVBG3DplrCo5EnCRCTx0DhDo7sNuHx2ABzuN/yd/r5pzlSaQOOtuaOyh0gZx1XxxRxZIpdfGCJ+tuHfN1FNXYMFO7gyG4s38cGGML9lrv5mfiHzVOpXixODOSP5A6Qs07LuIsYAJmoAvFIgCBkTMCbY2xA1rjf8tfbX9G5mK9TqV4sjrbmj+QOkLcOq2OKGgCZqMbj/DuAOEWMDabHHybgQHG43/K3YuPdmj3wOpXqpnFiIHckd4CctauOaTqJZwBsK68FEA98AxCniLHBivEnRfwxnYgCnOfZfM/GMaE8PKISlerGcWIgfyR3AmfjAOyjZtUx7Sbx9QGwfPqU5nJ4W5bLcl0Acf4dQJwixgYLxp+kE3ArElGA43xa8No8JlCpbgc+h3yR3AmYzQNwMNpM4usDYH+lounp+IfBBSvHBRDn3+GrPKvdfFiYtFPE2GDL+JNoAm5BIgrwQatNQKfGVgvHhOjYlE4+t1vzRw670YcFce7aQiIkd0Jm4QAcGlsm8S7Ks+84/w4f5ZXQD2mjoIixwaXxhxgG5MfFsdW2MaHeh7MO9WERXLy2kEyP6QbAHNsG4BA1m6zbOIm3Ta59t2FT7bx7I4fPvyN/0bEpRXvGNf/YQ4r2jNd2xGzTKqFv499royLGBofGH2IYkKMmY2v10QetjTPWjQkhxac02vSLE3MaxKJyJ2Au7Q56y7OH6BUqx77z6fw78ufKDlheCf2QNgqKGBucGn+IYUBumo6hp06qun+flXHGtjEhpPiURqt+cWVOg3gkd0Jm2QAcIqcm8ZbJu+944BsSc+SIa14J/dA2CooYG1wZf4hhQH6aja3nWRhnbBsTQotPSbXsF0fmNIgXbHKHh0jZNwCbZPJ6cGUSbyP6DjZwZmcwr4S+4Y2CualDip79QfBxzBTGYSAncWPrItbFGVk2JnQQn4JYI7bol+r/+UHsj9h4rWGpIJM7lJtdYNUAbAjXQzaCCIZADFd2BvNK6JvcKIiOTenE9/9e1SPvSWL8BpCMC3OWBWPr71+TTp1c8j22xRnb1Ptw2UsvaDbB27KSrAlcuHbaaRW3I0fmNIgXZHKHcjMswPXQNRJkCJpDR1zzSugb2yj4yY81/2Fi5zzGbwAtuDRnqY+ti9ssydo4Y5uewWGt3LJd56an239zmzWBS9dOO03jtkNzGiwV5NuynCmhRyG4HjLA2wgQsJ7BYZW27FBpdL107XUqja5XycGJnosYvwGk5uCchThTjLYxxcFrJy2uNbcFWbnjSgk9isH10D0WWAgdR1zNYPwGkJarc5akcabx2NDJoTWKbr2NhXlC7WKKq9dOWsxp3BVk5Y42bKqVlzWi3CxcXA9da7aQYoEFIFcbNql3aO3CrzF+A2jB5zlL/dhQdf8+aXJCsy//u6q7ttUSPmivzZrA52sHfgiycoe3RKER10MGOJ8LwICewWGt2v59zfC2LABJ+Txn4TmSXWm7JvD52oEXgkzuSJSbYSGuh+6QIANgSnl4RD2M38iAD2/BQXs+z1lCOTaUp1ZrAp+vHfgh2OROiJi0IE8kyAAgP8TwfPn0Fhy05+ucheeQ5c/Xa6cR8cZdJHcCwaQFAAA3EcML0OQ4S/Vf90j3PWymTUBaHBtCl4g3bgvzgcohCuDVfQAAeIkYnrumx1Z+/1seRgujomNTivaMa/6xhxTtGW95PS5+jfXyz32R11gjHeKN06jcCQRncAEAcBMxPH/NjrPo3DkeRgtjOqmiaDw2tLJS0fT0dEGthQ+IN24juRMIzuACAFCcLJ9ZQAwvwIZN0q9fkebOLflfLGrc5+wzRHj7FQpGvHFb8MkdZwf7tDiDi4wFc+8AQEqZP7OAGJ67nsFhzX/qL6X/+s8l/49FjdtcfoYIVRQoXADxxuc1TNDJHZcH+7R4dV9zPt/geQnp3gGA1DLebSeGF6P09btUPfRHrxc1QXK4+oUqChSlcT2kkStr/82e8S7ezE0d8noNE3Ryx+XBvhMhvLovLZIUHWr2VpFHH1T0yRu8CgIAkFYeu+1Zx3A2NpYiieYnp6tfAqiigHmL10OSpA8fzu3b+Hf6+ae9Xv8nTu5EUaStW7eqv79fW7duzbNNhXF6sEc2AkvwZaXpPXLqpKr795EgC5SPcQLohO277WxsNMdGWL5MxAnb78dWSDj6xdqkekDrofmZ+AeM+7L+T5zc+fnPf661a9fqzJkzebanUC4P9shmgCTB15mmbxWp8zQgoDUf4wTQEdt32wOayMMuRuKE7fdjGyQc/WBzUj2k9VBvf0VLH5vvz/q/J8k3HT9+XL/5zW90yy235N2eYm3YVBvcGzk02IesPkBW9++TJidU3b9P1V3bagmfFJrdyL7c4EWVg0gAACAASURBVLmJu3cW8TEgoDlv4wTQgZ4Py9lLo+ula69TaXS9VeXtIU3kYQ9TccL2+xGBaJVUNyyk9dCKjXcXsv6Pjk0p2jOu+cceUrRnPPUatVOJKneeffZZfeMb32iZZd+7d6/27t0rSdq5c6cqlUrnjSqXu/r5xCoVze3YrdPPP635mWn19le0YuPdKg+P5P+7EyisHyzWrA9OPrdbszED5LKXXtDKLdsT//1zm+/XiXfe1vyR985/rXdorVZtvl9li/reumuh4d45+1+vqnry/SXfsnxojVZm3Gbr+gHntYsTWcYIiWuhjn6wuA8qFekTjxb269L0w8mhNZqdnFjy9TzG7SJZey1AkuE4UfD9aAvuiRob+mHm9KnYipHy6VPqL6htzfrBxvXQ3NShXNbo5XJZAzmv/+emDunE9//+fH9WJfW+87ZWbf9+7nmGtsmdX//611q5cqXWrVunN954o+n3jY2NaWxs7Pyfp6fjz7MlUalUuvr5VMp90h33SZIiSSckqajf3Uah/WCpZn0wf+Rw7PfPHjmsc2n6rNyn6Nt/p1LD8a5owyadKPdZcx1Ill4L9Xvn1ikp5iFsZ2+9LfM2W9kPKY2M2JE8zlKSOJFljJD8uBayQD/QB3Vp+iG69TbpwOuFjNtF8uVaIE7UhBonsnwui6t9kDUb+iFacUns1+dWXFJY25r2g2XrocVH2M5Jmj3weiYVd5VKpfbvynH9Hz37A1UbEmWSNH/kPc08+wP1ZHTEslmcaJvcmZyc1K9+9Sv99re/1QcffKAzZ87oiSee0Le+9a1MGgakUQ94OvTH2P/fSfkgZ5m7w8P+QJwA3MK4jaIRJ5Kx+bks6JLlz36yaj3k+HPhTB59bpvcuf3223X77bdLkt544w399Kc/ZSCGEbGv6Wtk0QAZGqsCAgpnU5yw9k0UgGUYt1Ekm+KE1VosaqMNm4hvDiOpnpzrz4Uz+dKmxG/LAoyLC3iSdMlKlT55AwMkEDh2PIEakpyAm5ouao8eXnAEnvjmJpLqyTj/RmuDVVqpkjuf+tSn9KlPfSqvtgAtNc3WjlyZ2flFAN0xGiccL+MFskCSE7ZjPdFcs0Wt/t8J6fjRhV8jvgUnmMS95UfY2jFZpUXlDpzhfBYXQK5cL+OFH4xPvklyAu5qtqj9i5VLkzsivoUkpMS9D0fYTFVpkdyBOxzP4gLIFwlgmGbD5JskJ+CuZota/eTHqh6cXPL9xLdsGU/OtxJY4p4jbJ1xKrlj9Q2H3PmQxQWQIxLAMM2CyTdJTsBtcYvaiPiWOxuS862QuEcSziR3bL/hUAyyuACaIQEM06yYfLMIBLxDfCuABcn5VkjcIwlnkju233AAAPNIAHeGyths2DD5ZhEI+In4li8rkvOtkLhHAs4kd6y/4QCPsfAD/EVlbIYsmXyzCASAdGxIzrdC4h5JOJPcsf2GA3zFwg/wHJWxmWHyDaAVNsssZklyvhUS92jHmeSOCzcc4CVPFn5MqIB4VMZmi8k3gDhsltkt1OQ882O/OJPcCfWGA0zzYeHHhApozrXK2MUT0bnN90vlPtPNAoDWPNks81loyXnmx/5xJrkjhXfDATZwbeEXiwkV0NyGTdJbv5dmjl34Wv+glZWxcRPRE++8rejbf8dEFMASNlUl+LBZBs8wP/ZOj+kGALDchk21I5CNHDsSyYQKaKNabf1nW8RMROePvFf7OgA0mJs6pOqubaru3ydNTqi6f5+qu7bVEj4GNNsUc2qzDF5hfuwfpyp3krApQw/4wIcjkV5UHwF5+cmPpfenF37t/Wkrd+6YiAJI6vTzT9tVlcDzQ2EZX+bHrP8v8Cq5w7lBIB/OH4lkQgU05VLCJK+JqE0TQ5vaArhsfmY69uumxjYfNsvgGQ/mx6z/F/IqucO5QQBxmFDBRrYs4p3auYuZiPYOrVXUxUTUpomhTW0BXNfbX9G5mK+bHNuc3yyziC0x1GVezI9Z/y/gVXLHpd1HAMViQgWbWLWId2jnLm4iumrz/TrRzduyMpoYZrLQYJIKZGbFxrs1e+B1J8Y2pGNVDHWc6/Nj1v8LeZXccWr3EUBh2N2BdTJYxEfHpnTyud2aP3K4q+vatZ27xRPRcqUiTccfv0gii4lhVgsNJqlAdsrDIyo5NLYhBRLh+BDr/4W8Su64tPsIoBjs7sBG3S7i69f1bEbXtes7d93IZGKY0UKDSSqQLdfGNjajkrEtEc7nZhDr/wW8Su64tvvYSlY7siFgQEVLTRZd1fGHFT3wD1wrMKLrRTy7ltnJYGKY2UKDSSoQLDaj2qvP+XXoj7H/30QinM8tuTzWbD6t/7PgVXJHci9DHyfrHVmfMaCinaaLq+NHVd21jWsFZnS5iLdt19JlWUwMs6q4YZIKBIykfUuL5/xLmEqE87klkueazYf1f1a8S+54gUEiOfoKbTRbdEniWoEx3S7iOb6Tra4nhhlW3DBJBcJE0r6NuDm/JF2yUqVP3mAsEc7nlhBrtkKQ3LEQg0Ry9BXailt0NeBagSldLeI5vmMVKm6S4yg1EI+kfWtN52sjV6rHYHKAzy0Z1mzFILljIQaJ5OgrtFNfdFXHH5aOH13y/7lW4KL6db3spRc0y7PZrEDFTXscpQZaIGnfkrVzfj63RKz9/DxDcsdGDBLJ0VdIoGdwWNED/7D0rDbXChzWMzislVu261wXrwEHksqk4oayfKCpJBWAQVe+WTrnp3IzIUs/v6RcufdI7liIHdnkGFCRVNy1Uv2rL0o/+bHmuXYAoKmsKm4oywdaa1UBGHrlm81zfio327P582vHpXuP5I6l2JFNjgEVSTVeK9GxKWnXNlUdGKgBwKiMKm4oywe6QOUbc37HxX1+TlTEOHTv9ZhuAAAY0WqgBgCcl1nFzYZNtTL8Rg6V5QMmUfkG39QrYqr790mTE6ru36fqrm21hI9FXLr3qNzxgBMZT8AyLg3UAGBSVhU3LpflA6ZR+QbvOFIR49K9R3LHcS6dAQRs4tJADYSEDQsLZfggTI5VAB1y/IG0wGLObLQ6dO+R3HGdIxlPwDoODdRAKNiwsBMVN4B53IfwjSsbrS7deyR3HOdMxhOwjEsDNRAMNiysRcUNYB73Ibzi0EarK/ceyR3HuZLxBGzkykANhCLUDQuOogEAQsNGa/ZI7rjOUMbTpYmoS23FUo2f38mhNYpuvY3PD/BUiBsWHEUDAITK541WE2tQkjuOM5HxdGki6lJbsdTiz292ckI68DqfH+Arh0q0M8NRNAAAvGJqDUpyxwOFZzxdmoi61FYsxecHnBe3A6RKxXSzEkuygxViiXaoR9EAAPCWoTUMyR2k5tJE1KW2Yik+P6Cm2Q7Q3I7dUrnPaNuSSLODZVOJdhEl1SEeRQMAhCekR2WYWsP05Pq3w0vNJpw2TkRdaiuW4vMDPtRkB+j080+baU9arXawLFVPSFX375MmJ1Tdv0/VXdtqk9MsbdhUO3rWyPejaACAoBQWUy1hag1DcgfpuTQRdamtBYuOTSnaM675xx5StGfczsGVzw+Q1HynZ35muuCWdMbJKryCElI9g8Mqbdmh0uh66drrVBpdrxLPFQMA+MTBTZ6uGFrDcCwLqbn0TASX2lqkNEckTJZQLv78lg+t0VneloUANTu609tfUVR4a9Jz8ehRkQkpm46iATArpKMrCIeTmzxdMLUGJbmDjrg0EXWprYVJ+JAvG9421vj5raxUND3tRqUCUJfJRL3JW6RWbLxbJ7Jtbj4cfAuWiwkpAG6zYd4F5CHEmGpiDUpyBwhQ4uw5b6sCupLVRL3ZDlB5eERyIOHpZBWlIwmpevJw5vQpRSsusb9fATTHvAu+ciSmLuZaJZ11yZ3o2JROPrdb80cOW9GBrn2gCFPa6zRp9jy0EkogcxlO1F2vQnSt/S4kpBqTh+fqX2SXH3AW867sNM6NTw6tUcSxfqNciKmLuVhJZ1Vyp96Bs5Z0oIsfKMITHZtS9X//T+n92u59VZLefEPRg//Y/DpNmD0PsYQSyBIT9fzNTR1S9OwPcpksWp+QYpcf8ArzrmwsXsPNTk5IB15nDWeY9TF1sZQx1oaiELvelmXbU7Rtaw8Qo/qve84nds57f7r29SYSv52Ft1UBXTH1KsxQRMemdGL7t4N5tepiJA8Bzzg277L2zaus4ZCBNDHWlle9W1W5Y9skxbb2ALH+ezLd1z+UJHvuYgklYBVHz5g74yc/1vyR9xZ+LaDKFVO7/DbsTgI+cmneZfMJB9ZwyEKqGGtJJa1VyR3bShFtaw9ggnMllIBFXJqouyj4CbyB5KHNCzrAB87MuyxZzMZhDYdMpIixtsxH2iZ3pqen9eSTT+rEiRMqlUoaGxvTl770pXxaY9sOp23tgfc62g1dd630X/8Z//Uifj+CV2iccJAzE3UHhT6Bb0welk+f0lwRb8uyeEEHexEn/GPLYjYWa7hMhbo+SLNBZ8t8pG1yp7e3V3fccYfWrVunM2fOaOvWrfr0pz+tyy+/PPPG1Dtw2UsvaNaCt2Wx44oitdoNVaXS9OdKX79L1XcPSjPHLnyxf1Clr9+V2e/nmkcrRcYJ8AaQBTZsUu87by88mhXYBL6ePOyvVDQ9Pd3+B7pk9YIO1iJO+MeWxWycxWu45UNrdDbkWNmF0NcHiTfoLEkotk3urF69WqtXr5YkXXTRRVq7dq1mZmZyG4x7Boe1cst2nStggpIEO65+cCLj3Go39BOPNv2xnsFhRd95pPt/H7ux6FDRcSJkvAFkoZ7BYa3a/n3N5PS2LCxl84IO9iJOeMiSxWwzjWu4lQUlv73E+iARW4pCUj1z5+jRozp48KA++tGP5tUeIHOuZJy72Q3NIgnJbiyyQJzIGZOsJcrDI+oJ9N9uhOULOtiPOOEHWxazyBfrg+RsKApJnNyZnZ3V+Pi4Nm/erIsvvnjJ/9+7d6/27t0rSdq5c6cqLY6RtG1UudzVz/uCfsimD04+t1uzMYuhZS+9oJVbtnf1d2fp5NCa2i78IsuH1hRyLbT6/SstuQ65J+zWKk5kGSOkcK+FmdOndC7m6+XTp9QfYH9I4V4LixXWD5WK5nbs1unnn9b8zLR6+ytasfFulYdH8v/dbXAt2I84kc7c1KGu7rXc+6BSaVldbgsfroUsdNIPLqwP0vD9WkiU3Jmbm9P4+Lg++9nPanR0NPZ7xsbGNDY2dv7P3ZS+VSidk0Q/SNn0wfyRw7Ffnz1y2Jrjf5IU3XqbdOD1JbuhZ2+9TXNzc7lfC61+vy3XoQ/3xMiI+QVQHtrFiSxjhOTHtdCJaMUlsV+fW3FJkP0hhXstLFZoP5T7pDvukyRFkk5IkgWfgS/XAnGiJvQ4sbjy/Jyk2QOvq5Si8tz1PsgK/VDTST+4sD5Iw5droVmcaJvcqVareuqpp7R27Vp9+ctfzrxhQN5ceT6A6fJW078f7iJOFIgjMQAcRJzoAMdwYQHWB25pm9yZnJzUyy+/rCuvvFIPPvigJGnjxo268cYbc28ckAmHFkPdnNXM4qHRNpwVhXuIE8XhDSAAXEScSI9nncAWrA/c0Ta58/GPf1z/9m//VkRbgFyEkHF25aHR8BNxoli+vAHEibcYAsgEcSI9VyrPi0bsyA596Z9Ub8sCXOV9xpnSXQAOISENAG04VHleFGJHduhLPzmX3GmXYSQDiRBRugvAKU0S0tXxhzVfGSJ+AwheCJXnqbGZmR360ktOJXfaZRjJQNqLpFu+KN0F4JKmiefjR6XjR4nfjiPmA9nwvvI8JTYzs0Nf+qnHdANSaZVhTPL/YUQ96Vbdv0+anFB1/z5Vd22rTf46/PuiPeOaf+whRXvGO/57vLJhU61Ut1HgpbsA7JUo8Uz8dlLWMR8A6prFDjYz06Mv/eRUcqddhpEMpKUyTLoxaYzXMzis0pYdKo2ul669TqXR9Sqx4w3AVnEJ6RjEbwex0QYgL2xmZoe+9JJTx7LaHT3haIqdMk26cT60KUp3Abhi8bMkNH2kdiRrEeK3e9hoA5AXnkOUHfrST04ld9o+NZ6nylspy6Qbk0a78FwFAJ1qTEgvfmaeJOK3o9hoA5AnVzczbZwzu9qXaM6p5E67DCMZSEtlmHRj0mgPHmAOICvEb4+w0QYACzBnRlGcSu5I7TOMZCCz122mOdNJO5NGe3BEDkCGiN9+SBrzbdzFjuNKO9EanyOMYs6MgjiX3EGxsso0ZzVpZ3fXHhyRAwDEaRfzXdnFdqWdaI3PMUyNCb2TQ2sU3Xqbsc+bOTOKEmxyhwx+QhZmmtndtQNH5AAAHbFwbhHLlXaiNT5H62W9Lluc0JudnJAOvG4socecGUUJMrlDBj85Ms1oiiNyAIAOuDK3cKWdaI3P0W65rMtsS+gxZ0ZBgkzuWHfDW4xMM5rhiBwAoBOuzC1caSdaM/k5clIggRzWZbYl9JgzoyhBJndsu+GtRqYZLXBEDgCQmitzC1faidYMfY6cFEgmj3WZjYlZ5swoQpDJHRtveFuRaQYAAFlyZW7hSjvRmrHPkZMCieSyLusgoUeVFXwQZHKHnZh0yDSbFR2b0snndmv+yGGCDQDAC67MLVxpJ1oz8TlyUiChHNZlixN6y4fW6GyLt2VRZQVfBJncYScGrqgHm1mCTa7YrQEAAFnipEAyea3LGhN6KysVTU9PN/9mqqzgiSCTOxI7MXAEwSZ37NYAAIDMcVIgMdPrMqqs4Ise0w0A0BzBpgCtEmgAAAAd6BkcVmnLDpVG10vXXqfS6HqV2DiyUrNqKqqs4JpgK3fywNEOZI2S3vyRQAMAAHkwXZGChKiygidI7mSEox3IBcEmdyTQAMBveW2+sakH+KHb5/7kPRYw1iApkjtZ4dkoRvk66NWDzbKXXtCs42/LsvYzIoEGwHLWjp8OyGvzjU09wC+dVlnlPRYw1iANkjsZ4WiHOb4Pej2Dw1q5ZbvOtXrKv+Vs/ox4ex7gF98SITaPn07Ia/ONTb0g+DaeIAd5jwWMNUiB5E5GONphEIOe/Sz/jDgTD/jBy0SI5eOn7fLafGNTz39ejicWczWRlvdYwFiDNHhbVlY2bKod5Whk4dGO6NiUoj3jmn/sIUV7xmsDqeMY9OzHZwSgEB6+/Y7xszt5vQWHt+sEwMPxxFb1RFp1/z5pckLV/ftU3bXNiXVK3mMBYw3SoHInIy4c7fB1B4KqKfvxGQH+smm31cdECONnl/J6rhrPa/Oej+OJtVyuUMx7LGCsQQokdzJk/dEOlwfOVhj07MdnhALYlGQIhW2bBnkkQhZfV9W/+qJK//HvxV1njJ9dyWvzzYVNPXSHxGpxXE6k5T0WMNYgDZI7AXF54GyFQc9+fEbIm21JhmDYtmmQcSIk9rp69T9UjeYv/Dnn64zxs3t5bb5Zv6mH7hhKrIa4UeF6Ii3vsYCxBkmR3AlIs4FTh/6oaM+408GDQc9+fEbIlW1JhkDYtmmQeSIk7rr6MLFzXgHXGeMnUIwliZW/vb/QSr1gNyqoUAQyQXKnCS+z5nEDpySdOll7gFkIwQNIwctxwFO2JRlCYeNua5aJkKTXD9cZ4L5miRVt2aHeomJ/oBsVVCgC2SC5E8PXrPmCgfP3r0mnTi78hgCCB5CUr+OAr2xMMgTB893WphWvMd8HwHEWJFZC3qigQhHoHq9Cj+Pxqw97BofVc9cD0siVsf8/hOABJOLxOOClDZtqSYVGHiUZbNUzOKzSlh0qja6Xrr1OpdH1KvmUAI27rnp6F/6Z6wzwgg2JFV57na3o2JSiPeOa+V/3Kdoz7sSr1YFuULkTw4bBPW/scgOthTAO+KSbkm6O33XH593WuOuq8LdlASiEFXNjz6shs5A0ZjdWYJ+rf5EKbHiO5E4MKwb3vBE8gJaCGAc800mSgeN37jCVhIu9rj5+Xe6/F0DBLJgb8+yZ1lLFbAuO2QFFI7kTx4LBPW8ED6CNAMYBiMmfI1pN6FWpGG0XcRTwgy1zY5+rIbuWImZTgY0QkdyJYcvgnjeCB9BcKONA6Jj8OaLVhP4TjxppElVfgH+YG9stTcymAhu2KWJDiOROEwzuABgH/Mfkzw1WJuGo+gKAQqWK2VRgwyJFbQjxtiwAQLh4y5YTbHyDjJUJJwDwWYqY3fg2x4/8jxv9e5sj3FLQW3ip3AEABIvjd+akKk+2cAeWqi8AKFbamF2vwO6vVDQ9PV1wa4ELitoQ8iq5w4MNgXBx/6NTHL8rXtryZCuTcBYmnAAgjk9zJGJ2uFy+jovaEPImucODDYFwcf/DNy5PYBLp4Hk1tk3orUw4AQja4tgxt/l+Re/PMEeC85yf6xe0IeRNcocHGwIB4/6HR5yfwCTgy/NqbEs4AQhXXOw48c7bqg6vZY4E9zk6129MuGrkytp/s2d4W1Y7vkwUAaTH/Q+vODqBSYPn1SBP3le+IXdOXkMxsWP+yHvSn/8U++3MkeASF+f6ixOukqQPH/Sd13jiTXKHiWLYnAzCyAz3P3zi4gQmNZ5Xg5yEUPmGfLl6DaWNEcyR4BIn5/oGNuv8eRU6r7MNVj0IV/fvkyYnVN2/T9Vd22oJH4SB+x8esfG131lrfEWtrr2OV9QiOwW9bhYec/Qaahoj1l3LHAnuc3Cub2KzLlHlzmuvvaZnnnlGURTplltu0Ve/+tXcGtQpHmwYsACOMKA17n/zXIgTzgikqoXn1SAPQVS+OcqVOOHsNRQTO3qH1ir6+l21PzBHgsNcnOubqDZqm9yJokg/+tGP9PDDD2tgYEDf+973dNNNN+nyyy/PrVGdYqIYJmeDMDLF/W+OS3HCBS5OYABbOFm6HwCX4oSL11D98QT6i0ulKJJWrlZpcFirNt+vE+W+2jcxR4LjnJvrG9isa5vcefvttzU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            "text/plain": [
              "<Figure size 1440x360 with 3 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9O4h6hO0l7Tq"
      },
      "source": [
        "And if there is some randomness, but not complete, then less information is gained, and it has less entropy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "id": "eV7EynvdmD2Y",
        "outputId": "a609dbae-aaff-42e7-aa9a-8d9e72fd2be3"
      },
      "source": [
        "fix, axs = plt.subplots(1, 3, figsize=(20, 5))\n",
        "\n",
        "for ax in axs:\n",
        "    x, y = np.random.normal(loc=4.5, scale=1.0, size=100), np.random.normal(loc=4.5, scale=1.0, size=100)\n",
        "    ax.scatter(x.ravel(), y.ravel())\n",
        "    ax.set_xlim(-0.5, 9.5)\n",
        "    ax.set_ylim(-0.5, 9.5)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1440x360 with 3 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4kS6_5U8mV2m"
      },
      "source": [
        "## So how to define Entropy?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hBnD4sCTmZML"
      },
      "source": [
        "Entropy is defined as the shortest expected length sequence that can contain the information of one experiment.\n",
        "\n",
        "$$\\text{Entropy} = -\\sum_i \\log(P_i) $$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_01JgAOtmpmU"
      },
      "source": [
        "Here is an example of a tree that tries to actually show this bound, called the Huffman tree. The more frequent letters like A have the shortest code, just call it 0, and the less frequent ones have longer code. We can show that to minimize the expected length of the code, that is the probability of the code times the length of the code averaged over all letters, the best result we can get is the bound shown above."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cC2yQSdSkUKe"
      },
      "source": [
        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)"
      ]
    }
  ]
}