Built-in Mathematica Symbol

HypergeometricDistribution

HypergeometricDistribution[n, n_succ, n_tot]
represents a hypergeometric distribution.

A hypergeometric distribution gives the distribution of the number of successes in n draws from a population of size n_tot containing n_succ successes.

HypergeometricDistribution allows n, n_succ, and n_tot to be any integers such that 0<n≤n_tot, and 0≤n_succ≤n_tot.

Mean and variance of a hypergeometric distribution:

Probability density function:

Mean and variance of a hypergeometric distribution:

Probability density function:

Generate a set of pseudorandom numbers that are hypergeometrically distributed:

Properties based on higher-order moments:

Second moment of a hypergeometric distribution:

The

quantile of a hypergeometric distribution:

The probability of 25 successes in 50 draws from 100 elements that include 40 successes:

The probability of fewer than 25 successes:

The probability of more than 25 successes:

Plot the cumulative distribution function of a hypergeometric distribution:

The density functions of hypergeometric random variables are concentrated about their means:

The probability of getting an irrational number or negative number is zero:

The characteristic function of the hypergeometric distribution is defined in terms of Hypergeometric2F1Regularized:

HypergeometricDistribution is not defined when n_tot, n_succ, or n is non-positive:

HypergeometricDistribution is not defined when n>n_tot:

HypergeometricDistribution is not defined when n_succ>n_tot:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: