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**statmajor** Let Zn be a chi square distribution with n degrees of freedom. Let Wn = Zn/n^2. Find the limiting distribution of Wn.

I know the MGF of a chi square distribution is $\displaystyle (1 - 2t)^{\frac{-n}{2}}$

$\displaystyle E(e^{tW_n}) = E(e^{t \{Z_n}{n^2})= (1-\frac{2t}{n^2})^{\frac{-n}{2}}$

I'm trying to use the taylor expansion (1+b/n)^c = e^bc as n approaces infinity, but can't since the denominator is n^2, and not n, and I'm stuck here. I'm assuming I made a mistake somewhere, but can't figure out where.

Any help would be appreciated.