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

(i) Find the moment generating function.

Now I did moment generating function = E( so for continuous r.v =

.

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 is and find the expecation and variance of Y.