Could someone please assist on this homework problem. Please show work, thank you.

Problem 4. (10 pts.) An experiment includes two steps described as follows: Step 1. A random variable N has a Poisson distribution with probability mass: fN (n) = n! for n = 0, 1, 2, ..., and zero elsewhere with fixed > > 0. Step 2. Given N = n, a continuous random variable X has a gamma distribution with probability density: x(n+1)-10-x/b for x > 0; fxIN(an) = T(n + 1)62+1 . 0, elsewhere, where b > 0 is fixed. 1. Find E(X ). 2. Find Var(X)