Please help with the second question of this problem.

Given that N=n, the conditional distribution of Y is chi-square with df=2n. The unconditional distribution of N is Poisson(theta).

To show that (Y-EY)/sqrt(var(Y)) converges to a standard normal distributed variable in distribution

Given that N = n , the conditional distribution of Y is 222:1 . The unconditional distribution of N is Poisson(6). (a) Fine the unconditional mean E(Y) and variance Var(Y). (b) Show that, as 9 > oo , z = Y ' E(Y)_L_;N(0,1). Var(Y) (HINT: First find the moment generating function of Z.)