# Hypergeometric Distribution. Probability density function, cumulative distribution function, mean and variance

This calculator calculates hypergeometric distribution pdf, cdf, mean and variance for given parameters

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In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of *k* successes (random draws for which the object drawn has a specified feature) in *n* draws, **without replacement**, from a finite population of size *N* that contains exactly *K* objects with that feature, wherein each draw is either a success or a failure. In contrast, the binomial distribution describes the probability of *k* successes in *n* draws **with replacement**. Wikipedia

**Probability density function** of the hypergeometric distribution is

,

where

is the number of combinations of m from n or binomial coefficient

**Cumulative distribution function** of the hypergeometric distribution is

,

where

is the generalized hypergeometric function

**Mean** or **expected value** for the hypergeometric distribution is

**Variance** is

The calculator below calculates mean and variance of negative binomial distribution and plots probability density function and cumulative distribution function for given parameters n, K, N.

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