hypergeometric random variable

$X$ is a hypergeometric random variable with parameters $M,K,n$ if

$f_X(x)=\frac{\left(\genfrac{}{}{0pt}{}{K}{x}\right)\left(\genfrac{}{}{0pt}{}{M-K}{n-x}\right)}{\left(\genfrac{}{}{0pt}{}{M}{n}\right)}$, $x=\{0,1,\mathrm{\dots },n\}$

Parameters:

• $M\in \{1,2,\mathrm{\dots }\}$

• $K\in \{0,1,\mathrm{\dots },M\}$

• $n\in \{1,2,\mathrm{\dots },M\}$

Syntax:

$X\sim Hypergeo(M,K,n)$

Notes:

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. The expected value of $X$ is noted as $E[X]=n\frac{K}{M}$

3. The variance of $X$ is noted as $Var[X]=n\frac{K}{M}\frac{M-K}{M}\frac{M-n}{M-1}$

Approximation techniques:

If then $X$ can be approximated as a binomial random variable with parameters $n=K$ and $p=\frac{M-K+1-n}{M-K+1}$. This approximation simplifies the distribution 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