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

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

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

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