Question: Suppose the random vector (X1, X2, X3 ) has a multinomial distribution with m trials and cell probabilities p1, p2, p3. The joint pmf of

Suppose the random vector (X1, X2, X3 ) has a multinomial distribution with m trials and cell probabilities p1, p2, p3. The joint pmf of (X1, X2, X3) is m! PX1,X2,X3 (X1, X2, X3) = x1!x2!x3! PI P2 P3 . Show that the conditional distribution of (X2, X3 ) given X1 = x1 is multinomial with parameters m - x1 and (p2/ (p2 + p3), p3/ (p2 + P3))

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