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Hypergeometric Distribution
Consider a statistical experiment where a sample of n
observations are to be taken from a population of size N.
The population contains k items that are labeled
'success' and N - k items that are labeled 'failure'. If
a random variable X assumes the value equal to the number of
successes in the sample of size n, then X has a hypergeometric
distribution with parameters N, n and k.
The random variable X is said to be hypergeometrically
distributed with parameter N, n and k, and has
the following probability mass function:
The mean and variance of a random variable X that is
hypergeometrically distributed with parameter N, n
and k are computed as follows:
EX. In a certain game show, a contestant is asked to choose a
number of boxes from a set of 10 boxes. One of these boxes has a
prize, while the rest are empty. The number of boxes that the
contestant may choose ranges from 1 to 3.
The random variable X, the number of boxes chosen by the
contestant that contain a prize, will have a value that is either
0 or 1. It is hypergeometrically distributed with parameters N
= 10, n and k = 1.
If the contestant can only choose one box, n = 1.
If he or she can choose two boxes, n = 2.
If three boxes can be chosen, then n = 3.
As the number of boxes picked increases, the chances of
choosing the box with the prize increases.
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