Originally Posted by

**akolman** Hello,

I'm stuck with this problem.

Let $\displaystyle Z_n$ be $\displaystyle \chi^2(n)$ and let $\displaystyle W_n=\frac{Z_n}{n^2}$. Find the limiting distribution of $\displaystyle W_n$.

I tried getting the mgf of $\displaystyle W_n$ and then take the limit as $\displaystyle n \to \infty$ to the mgf of the limiting distribution

This is what I got, but I don't know if it's right.

$\displaystyle M_{W_n}(t)=\left( 1- \frac{2t}{n^2} \right)^{-\frac{n}{2}}$ for $\displaystyle t < \frac{n^2}{2}$.

I don't know how to arrange the mgf so I can get an e as I take the limit....

Thanks in advance.