# Question

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

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

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