If X1, X2, . . . , Xk have the multinomial distribution of Definition 5.8, show that the covariance of Xi and Xj is €“nθiθj for i = 1, 2, . . . , k, j = 1, 2, . . . , k, and i ‰  j.
Definition 5.8
The random variables X1, X2, . . ., Xn have a multinomial distribution and they are referred to as multinomial random variables if and only if their joint probability distribution is given by

For xi = 0, 1, . . . n for each i, where

(***) x*****Txlx f(x1,x2.....Xk; n,01,02....Ox):