Hypergeometric Distribution - Related Distributions

Related Distributions

Let X ~ Hypergeometric(, ) and .

• If then has a Bernoulli distribution with parameter .

• Let have a binomial distribution with parameters and ; this models the number of successes in the analogous sampling problem with replacement. If and are large compared to and is not close to 0 or 1, then and have similar distributions, i.e., .

• If is large, and are large compared to and is not close to 0 or 1, then

where is the standard normal distribution function

• If the probabilities to draw a white or black marble are not equal (e.g. because their size is different) then has a Noncentral hypergeometric distribution