Let X1, X2, and X3 have a multinomial distribution with probability function p(x1, x2

Chapter 5, Problem 5.165

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Let X1, X2, and X3 have a multinomial distribution with probability function p(x1, x2, x3) = n! x1!x2!x3! px1 1 px2 2 px3 3 , n i=1 xi = n. Use the results of Exercise 5.164 to do the following: a Find the joint moment-generating function of X1, X2, and X3. b Use the answer to part (a) to show that the marginal distribution of X1 is binomial with parameter p1. c Use the joint moment-generating function to find Cov(X1, X2)

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