Hypergeometric Distribution-ECO6416

Hypergeometric Distribution-ECO6416 - Hypergeometric...

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Hypergeometric Distribution The Hypergeometric (x; n, M, N) Distribution applies when we are sampling n items without replacement from a population of M successes and N-M failures. The hypergeometric distribution arises when a random selection (without repetition) is made among objects of two distinct types. Typical examples: Choose a team of 8 from a group of 10 men and 7 women. Choose a committee of five from the legislature consisting of 52 Democrats and 48 Republicans. The Concept of Hypergeometric Events The above Venn diagram depicts choosing a random subset of size r from n items of which M = m items belong in a particular category, the probability that x = k of the selected items belong to that category. The Binomial distribution looks at n trials "with replacement." The hypergeometric distribution is for the case "without replacement." Here p changes from one Bernoulli trial to the next. Specifically, we have a population of size N with M out of the N members being "Successes" and the remaining (N-M) being "Failures." We
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Hypergeometric Distribution-ECO6416 - Hypergeometric...

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