N things can have x of one kind and N - x of another kind {hypergeometric distribution}. Mean equals R*p, where p is favorable-outcome probability and R is favorable-outcome number. Variance equals R * p * (1 - p) * ((N - R) / (N - 1)). Terms equal (x! / (x1! * (x - x1)!)) * ((N - x)! / ((N - x1)! * (N - R - x + x1)!)) / (N! / (R! * (N - R)!)), where x is thing or event and x1 is number of things that are the same.
comparisons
Hypergeometric distributions approximate binomial distributions, if probability is less than 0.1 and number of things is large. Hypergeometric distributions approximate Poisson distributions, if number of things is large and favorable-event number divided by thing number is less than 0.1. Hypergeometric distributions approximate normal distributions, if mean is greater than or equal to four.
Mathematical Sciences>Statistics>Distribution
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Date Modified: 2022.0224