Let the joint probability mass function of X1, X2, . . . ,

Chapter , Problem 19

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Let the joint probability mass function of X1, X2, . . . , Xr be multinomial, that is, p(x1, x2, . . . , xr) = n! x1! x2! xr! px1 1 px2 2 pxr r , where x1 + x2 + + xr = n, and p1 + p2 + + pr = 1. Show that for k < r, X1 + X2 + + Xk has a binomial distribution.

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