Question: 8. Let X1, X2, . . . be independent, identically distributed random variables and let N be a random variable which takes values in the

8. Let X1, X2, . . . be independent, identically distributed random variables and let N be a random variable which takes values in the positive integers and is independent of the Xi . Find the moment generating function of S = X1 + X2 + · · · + XN in terms of the moment generating functions of N and X1, when these exist.

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