Q2.6 Consider a multinomial distribution of m discrete random variables as follows: a. Prove that the multinomial distribution satisfies the sum-to-1 constraint X1, ,Xm

Q2.6 Consider a multinomial distribution of m discrete random variables as follows:

a. Prove that the multinomial distribution satisfies the sum-to-1 constraint Í
X1, ,Xm Pr¹X1 = r1, X2 = r2, , Xm = rmº = 1.

b. Show the procedure to derive the mean and variance for each Xi (8i = 1, 2, : : : ,m) and the covariance for any two Xi and Xj (8i, j = 1, 2, : : : ,m).

Pr(X1, X2 = 12,..., Xm = 1m) = Mult(1, 2, m N, P1, P2, Pm) N! = r1!12! PPPm ... Im!