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**statmajor** Find the moment generating funtion of Yn = Xn/n, where Xn has a gamma distribution with parameters alpha = n, and beta.

$\displaystyle E(e^{tY_n}) = E(e^{t\frac{X_n}{n}})$ I'm stuck here. I know that the MGF of a gamma (in this case) is $\displaystyle (1-\beta t)^{-n}$.

The question I have is what to do with the 1/n. I'm pretty sure it works out to be $\displaystyle (1-\frac{\beta t}{n})^{-n}$, but I'm not sure why.

Would someone be able to explain this to me?

Thanks in advance.