## Quick Reference

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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