## Multinomial Distribution

Let a set of random variates , , ..., have a probability function

 (1)

where are Positive Integers, , and
 (2)

 (3)

Then the joint distribution of , ..., is a multinomial distribution and is given by the corresponding coefficient of the Multinomial Series
 (4)

The Mean and Variance of are
 (5) (6)

The Covariance of and is
 (7)