An insurance company receives i.i.d. claims where . Let . Suppose and

a) Find E(X), var(X): I got this part with and

b) Suppose that Xi is . Find the MGF of X:

I tried MGF(t)= because and the sum of independent variables' MGF is just the product of each MGF, but the results doesn't match part (a). Please help me out with this part. Thanks!