Question: 4. Suppose that X1, . . . , Xn are independent and identically distributed random variables with probability function for Xi given by P(Xi =

4. Suppose that X1, . . . , Xn are independent and identically distributed random variables with probability function for Xi given by P(Xi = xi) = p(xi) = e−λλxi xi! , xi = 0, 1, 2, . . . , n That is, the Xi’s constitute a random sample of n independent observations on X, where X has the Poisson distribution with parameter λ. Find the moment-generating function of the random variable Y = X1 + · · · + Xn.

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