hypergeometric random variable

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

$f_{X}(x)=\frac{{K\choose x}{M-K\choose n-x}}{{M\choose n}}$, $x=\{0,1,...,n\}$

Parameters:

• $\star$

$M\in\{1,2,...\}$

• $\star$

$K\in\{0,1,...,M\}$

• $\star$

$n\in\{1,2,...,M\}$

Syntax:

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

Notes:

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

3. 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 ${K\choose 2}< 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 HypergeometricRandomVariable 2013-03-22 11:54:12 2013-03-22 11:54:12 alozano (2414) alozano (2414) 11 alozano (2414) Definition msc 62E15 msc 81-00 hypergeometric distribution