ii. Distribution function of T

Let

then

(I used the fact that )

Then are independent, identically distributed rvs, and therefore I can multiply their MGFs to get

If I let k=2n, then this can be represented as

Now i need to find an error in above because this should be the 2xparameter in the expression... OR, could this still be a version of a chi-square distribution with some adjustment to [what? random variable? parameter?]