X has chi square distribution with 4 degrees of freedom, with pdf

$\displaystyle f_{X}(x) = \frac{xe^-\frac{x}{2}}{4}, x>0$

(i) Find the moment generating function.

Now I did moment generating function = E($\displaystyle e^{tx})$ so for continuous r.v =

$\displaystyle \int e^{tx}\frac{xe^-\frac{x}{2}}{4}$.

Do I leave this here? I do I have to integrate and what happens with the t? Should I isolate the t outside of the integral first?

(ii) If X1...Xn are independent, identically distributed random variables, with chi square distribution, with 4 degrees of freedom, show that the moment generating function $\displaystyle Y = \sum X_{i}$ is $\displaystyle (1-2t)^{-2n}$ and find the expecation and variance of Y.