# Math Help - Gamma distribution mgf

1. ## Gamma distribution mgf

Y has gamma distribution with α=n/2 for some positive integer n and β equal to some specified value. Using method of mgf, show that W=2Y/β has a chi-square dist. with n df.

I know what the mgfs of gamma and chi-square are. The part that is confusing me is the W=2Y/β and how to plug in the mgf's and such.

2. Obtain the MGF of W.

$M_W(t)= E(e^{Wt})=E(e^{2Yt/\beta})=M_Y(2t/\beta)$

So, insert $2t/\beta$ where you have t in the MGF of Y.