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(a) Suppose Y1 is a gamma random variable with parameters 1 and and Y 2 is also a gamma random variable with parameters 2 and

(a) Suppose Y1 is a gamma random variable with parameters 1 and and Y2 is also a gamma random variable with parameters 2 and . Assuming Y1 and Y2 are independent, use the moment generating function to find the density function of U = Y1 + Y2.

(b) Suppose Y1, Y2, . . . , Yn are Poisson random variables each with parameter . Assuming Y1 and Y2 are independent, use the moment generating function to find the probability function for W = Y1+Y2+ +Yn.

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