Stochastic Process Generating Function Practice
I don't understand how $G_{N}(s) = G_{M}(G_{Y_i}(s))$.
$N = Y_1 + Y_2 + Y_3 + ... +Y_M$, which to my understanding the main generating function should be of $Y$ and the sub should be the index of $Y$. Therefore, I think $G_{N}(s) = G_{Y}(G_M(s))$. Am I wrong and if so, how to understand the correct version of the answer?