Multinomial Distribution
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).
The mean and variance of 
are
The covariance of 
and 
is
 |
(8)
|
REFERENCES:
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 532, 1987.
Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, 1984.
