Question: Suppose that X1, X2, . . . are i.i.d. random variables, each of which has m.g.f. (t). Let Y = X1 + . . .

Suppose that X1, X2, . . . are i.i.d. random variables, each of which has m.g.f. ψ(t). Let Y = X1 + . . . + XN, where the number of terms N in this sum is a random variable having the Poisson with mean λ. Assume that N and X1, X2, . . . are independent, and Y = 0 if N = 0. Determine the m.g.f. of Y.

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