Question: uppose X and Y are as in Problem 2 except now assume = . This means X has mgf MX (s) = (1 s/) and

uppose X and Y are as in Problem 2 except now assume = . This means X has mgf MX (s) = (1 s/) and Y has mgf MY (s) = (1 s/) . Show that X + Y also has a gamma mgf and deduce its parameters. (See Slide 240 in the notes. Also see the examples on Slides 242-243.) [Recall that chi-square is a special case of gamma. The result here implies that the sum of independent chi-square random variables has chi-square distribution, with degrees of freedom equal to the sum of the degrees of freedom for the individual random variables. We will use this fact later.] 1

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