Hypergeometric Distribution

Consider a pool of $N$ machines which contains $M$ defect machines. Now $n$ machines are randomly selected, let $X$ be the number of defect machines selected. Then $X$ is said to have a hypergeometric distribution.

• Parameters
  • $N\in \mathbb{N},M,n\in [N]$
• PMF
  • $p(k)=\frac{\left(\genfrac{}{}{0ex}{}{M}{k}\right)\left(\genfrac{}{}{0ex}{}{N-M}{n-k}\right)}{\left(\genfrac{}{}{0ex}{}{N}{k}\right)}$
• Mean
  • $\frac{nM}{N}$
• Variance
  • $\frac{nM(N-n)(N-M)}{N^2(N-1)}$