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Tech Tips: Hypergeometric Distributions

Calculating Hypergeometric Probabilities

To find the hypergeometric probability of seeing exactly x white balls when drawing k balls from an urn containing m white balls and n black balls, or equivalently P(x)=mCxnCkxm+nCk


Calculating Cumulative Hypergeometric Probabilities

Suppose one wishes to find the cumulative hypergeometric probability of seeing x or fewer white balls when drawing k balls from an urn containing m white balls and n black balls, or equivalently P(X<=x)=P(0)+P(1)+P(2)++P(x)=0ixmCinCkim+nCk


Simulating Random Variables following a Hypergeometric Distributions

To simulate numbers randomly chosen from a hypergeometric distribution, such as the count of white balls seen when drawing k balls without replacement from an urn containing m white balls and n black balls ...