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

$V(X) = \dfrac{Mn(N-M)(N-n)}{N^2(N-1)}$.

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