1. The problem statement, all variables and given/known data
Let Xn have a gamma distribution with parameters alpha = n, and beta, where beta is not a function of n. Let Yn = Xn/n. Find the limiting distribution of Yn.
2. Relevant equations
3. The attempt at a solution
[tex]E(e^{tY_n}) = E(e^{t\frac{X_n}{n}})[/tex]
I'm stuck here. I know that the MGF of a gamma distribution (in this case) is [tex](1\beta t)^{n}[/tex]
I'm not sure with what to do about the 1/n in the MGF. Would it be just [tex]\frac{(1\beta t)^{n}}{n}[/tex]
Any help would be appreciated.
