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Solve the problems below using the moment-generating-function technique. Make sure to state the distribution and its...

Solve the problems below using the moment-generating-function technique. Make sure to state the distribution and its parameters.

Let X1, . . . , Xn be independent random variables, such that Xi ∼ Poiss(λi), for i = 1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.

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