Hypergeometric Distribution
The probability mass function of Hypergeometric distribution is
$$ \begin{equation*} P(X=x)=\frac{\binom{M}{x}\binom{N-M}{n-x}}{\binom{N}{n}},\;\; x=0,1,2,\cdots, n. \end{equation*} $$
Mean of Hypergeometric Distribution
The expected value of hypergeometric random variable is
$E(X) =\dfrac{Mn}{N}$.
Variance of Hypergeometric Distribution
The variance of an hypergeometric random variable is