Suppose that X1, X2,... is a sequence of positive

Chapter 6, Problem 7

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Suppose that X1, X2,... is a sequence of positive integer-valued random variables. Suppose that there is a function f such that for every m = 1, 2,..., limn Pr(Xn = m) = f (m), m=1 f (m) = 1, and f (x) = 0 for every x that is not a positive integer. Let F be the discrete c.d.f. whose p.f. is f . Prove that Xn converges in distribution to F.

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