Let Y, Y... Y be independent random variables such that each Y, has a gamma distribution...

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Let Y₁, Y₂... 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 ß. Prove that U = Y₁ + Y₂ +Y has a gamma distribution with parameters a₁ + a₂ + and B. For each Y,, the moment-generating function is my my (t): function for U is m(t) distribution with parameters a₁ + a₂ = ])=(a₁ + a2 + an and B. + +an F Since the Y,'s are independent, the moment-generating which is the moment-generating function for a gamma Let Y₁, Y₂... 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 ß. Prove that U = Y₁ + Y₂ +Y has a gamma distribution with parameters a₁ + a₂ + and B. For each Y,, the moment-generating function is my my (t): function for U is m(t) distribution with parameters a₁ + a₂ = ])=(a₁ + a2 + an and B. + +an F Since the Y,'s are independent, the moment-generating which is the moment-generating function for a gamma

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