csopi

2. follows immediately from the total variance formula.

var Z=E ( var (Z|N)) + var (E (Z|N))

E ( var (Z|N))=E(N var (X1))=var(X1) E(N) -- by fixing N, Z is a sum of fixed number of Xi-s

var (E (Z|N))=var (N E(X1))=[E(X1)]^2*var(N)