Assume that X is squared-Chi-distributed, which means that the moment generating function is given by:
Use the mgf to find E(X) and var(X)
The Attempt at a Solution
I know that m'(0)=E(X), and m''(0)=var(X).
So I find:
which gives m'(0)=k
Similarily, I find
which gives m''(0)=k^2+2k
However, in my textbook, it says that the variance of a square-chi distribution should be 2k, not k^2. Where do I go wrong?