hypergeometric random variable

hypergeometric random variable (plural hypergeometric random variables)

1. (probability theory, statistics) A random variable whose probability distribution is a hypergeometric distribution.
   • 1992, Norman Lloyd Johnson; Samuel Kotz; Adrienne W. Kemp, Univariate Discrete Distributions, page 67:

     Computer generation of classical hypergeometric random variables has been discussed in detail by Kachitvichyanukul and Schmeiser (1985).

   • 2005, Martin Buntinas; Gerald Marlowe Funk, Statistics for the Sciences, page xv:

     Chapter 6 introduces testing of hypotheses immediately after the study of binomial and hypergeometric random variables.

   • 2007, Purna Chandra Biswal, Probability and Statistics, 2008, Prentice-Hall of India, page 87,

     If ${\displaystyle \textstyle X}$ is a hypergeometric random variable, then the variance is ${\displaystyle \textstyle Var(X)=\left({\frac {M}{N}}\right)n\left(1-{\frac {M}{N}}\right)\left(1-{\frac {n-1}{N-1}}\right)}$.

   • 2017, Sheldon M. Ross, Introductory Statistics, Elsevier (Academic Press), page 250,

     Thus, whereas the expected value of the hypergeometric random variable with parameters n, N, p is the same as that of the binomial random variable with parameters n, p, its variance is smaller than that of the binomial by the factor (N − n)/(N − 1).