Epitech Maths Project
When ducks are disturbed by a sudden noise, they fly away almost simultaneously, leaving the pond empty. Chances that a duck will then come back after t minutes are given by the following probability density function:
f: [0, +∞[ −> R
t 7−> ae −t + (4 − 3a)e −2t + (2a − 4)e −4t
where a is a real constant between 0 and 2.5, which depends on external factors (such as temperature, day time, duck’s health etc.).
A study is being conducted about these ducks, and you are asked to compute and display the following, given the value of a:
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The average time after which ducks come back,
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The standard deviation of the ducks’ return time,
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The time after which 50% of all of the ducks are back,
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The time after which 99% of all of the ducks are back,
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The percentage of ducks that come back after 1 minute,
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The percentage of ducks that come back after 2 minutes.