MonteCarlo_sampling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cab123e2",
   "metadata": {},
   "source": [
    "We want to know average sum of rolling 12 six sided dice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1fb06efc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "180712b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "monte_carlo_trial = 10000\n",
    "number_of_dice = 12\n",
    "estimation = []\n",
    "for i in range(monte_carlo_trial):\n",
    "    suma = []\n",
    "    np.random.seed(i)\n",
    "    for j in range(number_of_dice):\n",
    "        dice = np.random.choice([1,2,3,4,5,6])\n",
    "        suma.append(dice)\n",
    "    suma_12_dice = np.sum(suma)\n",
    "    estimation.append(suma_12_dice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "6902c590",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.833948507657571"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(estimation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "fefbbe17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(4,4))\n",
    "plt.hist(estimation, bins=40, label=f'Estimation of the sum {round(np.mean(estimation), 2)}')\n",
    "plt.axvline(round(np.mean(estimation), 2), c='r')\n",
    "plt.legend()\n",
    "plt.title(f\"Small example of Monte Carlo sampling \");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}