Suppose that X1, X2, . . . are i.i.d. random variables, each of which has m.g.f. (t).

Question:

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.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...