[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

We have seen that if the generating function for the offspring of a

single parent is [math]f(z)[/math], then the generating function for the number of offspring after two generations is given by [math]h(z) = f(f(z))[/math]. Explain how this follows from the result of Exercise Exercise.