HypergeometricDistribution

The hypergeometric distribution: $n$ draws without replacement from a population of $ntotal$ with $nsucc$ successes.

HypergeometricDistribution(n, nsucc, ntotal)an inert distribution object — carries

n, nsucc, ntotal

, unevaluated.

Typed signatures

Type	Package	Applies
`(real<0..>, real<0..>, real<0..>) -> distribution`	`statistics`	always

Domain: Statistics

Details

$PDF(k) = \binom{nsucc}{k}\binom{ntotal-nsucc}{n-k} \big/ \binom{ntotal}{n}$ , exact.
$CDF(x) = \sum_{k=0}^{\lfloor x\rfloor} PDF(k)$ , an exact FINITE sum (not a closed form) — only answers when $\lfloor x\rfloor$ resolves to a concrete integer, otherwise stays unevaluated rather than build an unbounded symbolic Sum.
$Mean = n \cdot nsucc/ntotal$ , $Variance = n\dfrac{nsucc}{ntotal}\left(1-\dfrac{nsucc}{ntotal}\right)\dfrac{ntotal-n}{ntotal-1}$ , both exact.
RandomVariate samples via sequential without-replacement Bernoulli draws (exact, not an approximation).