Hypergeometric Distribution

We use the Hypergeometric Distribution to answer the following question:

  • Given total objects, where of them are considered successes, and in trials, what is the probability you draw successes without replacement, i.e. ?
title:Hypergeometric Distribution (Definition) 
We say $X ∼ HGeo(N,r, n)$, where: 
1. $X$ is the number of observed successes. 
2. $n$ objects are randomly selected from $N$ total objects without replacement. 
3. There are only objects of two types: successes or failures. There are $r$ successes.

p.m.f. of :

Expectation and Variance

If it was with replacement, we can convert to , the Binomial Distribution