| Parameters | |
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| PMF | |
| Mean | |
| Variance |
The model of an urn with black and white marbles can be extended to the case where there are more than two colors of marbles. If there are mi marbles of color i in the urn and you take n marbles at random without replacement, then the number of marbles of each color in the sample (k1,k2,...,kc) has the multivariate hypergeometric distribution. This has the same relationship to the multinomial distribution that the hypergeometric distribution has to the binomial distribution—the multinomial distribution is the "with-replacement" distribution and the multivariate hypergeometric is the "without-replacement" distribution.
The properties of this distribution are given in the adjacent table, where c is the number of different colors and is the total number of marbles.
Read more about this topic: Hypergeometric Distribution
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