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
It can be shown that for the Hypergeometric Distribution
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.