Let a set of random variates , , ..., have a probability function
(1)

where are nonnegative integers such that
(2)

and are constants with and
(3)

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

In the words, if , , ..., are mutually exclusive events with , ..., . Then the probability that occurs times, ..., occurs times is given by
(5)

(Papoulis 1984, p. 75).
(6)
 
(7)

The covariance of and is
(8)
