MAT 316 Lecture Notes - Lecture 5: Multinomial Distribution, Hypergeometric Distribution, Unimodality
Document Summary
Situation: there is a finite population of n items, r of these items are classified as successes, and the remaining n r are classified as failures, a sample of size n is taken without replacement. X = the number of successes in the sample of size n. Notation: x ~ h(n = , n = , r = ) Note: if the sampling were done with replacement, then x would have a bi(n, ) distribution. We have already seen several examples of the hypergeometric distribution. The jury problem as well as the black and white marbles in an urn problems fit the hypergeometric situation. You may recall that there are two completely different ways to find these probabilities: one using counting rules, and the other using ands & ors. To get a formula for the pmf, we need to take the counting rule approach. Derive the pmf of the h(n, n, r) distribution.
