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 ofN 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.)