Hypergeometric Distribution

Probability Mass Function:
- $P (X = x) = \frac{(\begin{matrix} # way to select X \\ out of D objects \end{matrix}) (\begin{matrix} # of ways \\ to select n - x \\ out of N - D \end{matrix})}{\begin{matrix} # of ways to \\ to select n objects \\ out of N objects \end{matrix}}$
- $P (X = x) = \frac{(\binom{D}{x}) (\binom{N - D}{n - x})}{(\binom{N}{n})}$
Properties:
- #tk
- Mean variance, etc…
Example:
- A warehouse has 10 machines, 4 all defective.
- A company selects 5 at random, what's the probability that all 5 are working.
- $P (X = x) = \frac{(\binom{D}{x}) (\binom{N - D}{n - x})}{(\binom{N}{n})}$
- $P (X = x) = \frac{(\binom{6}{5}) (\binom{4}{0})}{(\binom{10}{5})} = \frac{1}{42}$
Example:
- How to use hypergeometric with $3$ types when interested in $k$ red out of blue red and green
Example: STA256 Lecture 20#^17b226