hypergeometric distribution

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The distribution of the number of ‘successes’ when sampling without replacement from a finite population each of whose members is classified as either a ‘success’ or a ‘failure’. As an example, suppose that an urn contains N balls of which w are white. Suppose n balls are taken from the urn at random and without replacement, and let the random variable X be the number of white balls obtained. Then X has the hypergeometric distribution given by . The initial derivation of the distribution was published by de Moivre in 1711. The mean of the distribution is nw/N and the variance is . For large values of N the hypergeometric distribution may be approximated by the binomial distribution B(n,p), where p=w/N, since in this case sampling without replacement is approximately equivalent to sampling with replacement.

Subjects: Probability and Statistics.

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