Let S N = N k =1 X k , where the stochastic variables X k

Question:

Let S_N = ∑^N_k ₌₁ X_k, where the stochastic variables X_k ∈ N ∪ {0} are identical and independent,
each described by the generator function g_X(s). Furthermore, the stochastic variable N ∈ N is described by the generator function g_N(s) and g_S_N (s) denotes the generator function for S_n.