A.14 Hypergeometric distribution
X has a hypergeometric distribution of population size N, index n and parameter π, denoted
if it has a discrete distribution with density
The mean and variance are
Because
we see that p(X+1)> p(X) if and only if
and hence that if, as is usually the case, N is fairly large, if and only if
Hence, the mode occurs very close to the binomial value
As this distribution approaches the binomial distribution .
Tables of it can be found in Lieberman and Owen (1961).