Probability Mass Function of Hypergeometric Distribution

Theorem

The probability mass function of a hypergeometric distribution on a discrete random variable $X$ is given by:

$\map \Pr {X = r} = \dfrac {\dbinom M r \dbinom N {n - r} } {\dbinom {M + N} r}$

where:

$n$ is the number of trials

$M + N$ is the total population, consisting of $M$ satisfactory units and $N$ unsatisfactory units

$r$ is the number of satisfactory units drawn from the population without replacement.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hypergeometric distribution
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hypergeometric distribution