Hypergeometric Weiss2[1]

# Hypergeometric Weiss2[1] - IET 2227 HYPERGEOMETRIC...

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IET 2227 H YPERGEOMETRIC P ROBABILITY D ISTRIBUTION Page 1 of 4 revised 3/24/2010 I NTRODUCTION F ORMULA : The hypergeometric probability distribution is similar to the binomial distribution, except that the hypergeometric distribution is used when the population is finite and relatively small and the random sample is chosen without replacement. Because sampling is done without replacement the trials are dependent, thus invalidating one of the key assumptions of the binomial distribution. N represents the population size and n the sample size. Let x represent the number of items in the sample that possess the characteristic of interest, called the number of successes, and p the proportion of the population that is successful. (Therefore, Np is the number of successes in the population.) Since sampling is without replacement, each time a sample is drawn; one of the Np successes and one of the N items in the population are removed. Thus on the next selection, there are Np-1 successes in a population of size N-1. With each selection both the number of successes and the population size decrease by one. Thus the selection process produces a factorial.

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Hypergeometric Weiss2[1] - IET 2227 HYPERGEOMETRIC...

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