Hypergeometric distribution, Mathematics

Hypergeometric Distribution

Consider the previous example of the batch of light bulbs. Suppose the Bernoulli experiment is repeated without replacement. That is, once a bulb is tested, it will be set aside.

         If X   = number of successes, then

969_hypergeometric.png

It can be shown that for the Hypergeometric Distribution

884_hypergeometric distribution.png

It should be intuitively clear that if nM/N is small enough, the hypergeometric distribution may be replaced by the binomial distribution. In our development of the subject, we will do so if n/N £ 0.05.

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