Let Y, Y... Y be independent random variables such that each Y, has a gamma distribution with parameters a, and B. That is, the distributions of the Y's might have different a's, but all have the same value for . Prove that U = Y + Y +Y has a gamma distribution with parameters a + a + and B. For each Y,, the moment-generating function is my my (t): function for U is m(t) distribution with parameters a + a = ])=(a + a2 + an and B. + +an F Since the Y,'s are independent, the moment-generating which is the moment-generating function for a gamma