Hifumi's Study NotesnotesProbability and StatisticsHypergeometric Distribution

Hypergeometric Distribution

Tags

PAS

Cegep/2

Word count

93 words

Reading time

1 minute

Discrete probability distribution of the number of successes in $n$ Bernoulli trials without replacement
Follows a hypergeometric series

Not related to geometric distribution

Properties

\begin{aligned} P (X = k) & = \frac{(\binom{K}{k}) (\binom{N - K}{n - k})}{(\binom{N}{n})} \\ E (X) & = n \frac{K}{N} \\ V a r (X) & = n \frac{K}{N} \frac{N - K}{N} \frac{N - n}{N - 1} \end{aligned}

Where:

$N$ = population size
$K$ = number of successes in population
$n$ = number of draws
$k$ = number of successes drawn

Contributors

Changelog

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