hypergeometric random variable
$X$ is a hypergeometric random variable with parameters $M,K,n$ if
${f}_{X}(x)=\frac{\left(\genfrac{}{}{0pt}{}{K}{x}\right)\left(\genfrac{}{}{0pt}{}{MK}{nx}\right)}{\left(\genfrac{}{}{0pt}{}{M}{n}\right)}$, $x=\{0,1,\mathrm{\dots},n\}$
Parameters:

$\star $
$M\in \{1,2,\mathrm{\dots}\}$

$\star $
$K\in \{0,1,\mathrm{\dots},M\}$

$\star $
$n\in \{1,2,\mathrm{\dots},M\}$
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 $Var[X]=n\frac{K}{M}\frac{MK}{M}\frac{Mn}{M1}$
Approximation techniques:
If $$ then $X$ can be approximated as a binomial random variable^{} with parameters $n=K$ and $p=\frac{MK+1n}{MK+1}$. 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  20130322 11:54:12 
Last modified on  20130322 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 8100 
Synonym  hypergeometric distribution 