hypergeometric random variable

fX(x)=(Kx)(M-Kn-x)(Mn), x={0,1,,n}


  • M{1,2,}

  • K{0,1,,M}

  • n{1,2,,M}




  1. 1.

    X represents the number of “special” items (from the K special items) present on a sample of n from a population with M items.

  2. 2.

    The expected valueMathworldPlanetmath of X is noted as E[X]=nKM

  3. 3.

    The varianceMathworldPlanetmath of X is noted as Var[X]=nKMM-KMM-nM-1

Approximation techniques:

If (K2)n,M-K+1-n then X can be approximated as a binomial random variableMathworldPlanetmath with parameters n=K and p=M-K+1-nM-K+1. This approximation simplifies the distributionPlanetmathPlanetmath by looking at a system with replacement for large values of M and K.

Title hypergeometric random variable
Canonical name HypergeometricRandomVariable
Date of creation 2013-03-22 11:54:12
Last modified on 2013-03-22 11:54:12
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 11
Author alozano (2414)
Entry type Definition
Classification msc 62E15
Classification msc 81-00
Synonym hypergeometric distribution