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Hypergeometric Distribution

Consider a statistical experiment wherein a sample of n observations is to be taken from a population of size N. The population contains k items that are labeled ‘success’ and N – k items that are labeled ‘failure’. If a random variable X assumes the value equal to the number of successes in the sample of size n, then X has a hypergeometric distribution with parameters N, n and k. The random variable X is said to be hypergeometrically distributed with parameter N, n and k, and has the following probability distribution:


Mean (µ) of the Hypergeometric Distribution:

µ = nk/N

Variance (σ2) of the Hypergeometric Distribution:

σ2 = [(n)(k)(N-n)(1-k/N)]/[N(N-1)]



De Silva, S., D’Andreti, P. (1997). Discrete Probability Distribution – HYPERGEOMETRIC DISTRIBUTION. Retrieved December 2, 2006 from http://library.thinkquest.org/10030/6dpdhd.htm.



1. me - April 17, 2011

i have this example with me, but yet i have no idea how to do the calculation for the P(X) formula as mention above. please guide.

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