3.9.10 Suppose that in a branching process the number of offspring of an initial particle has a distribution whose generating function is f .s/. Each member of the first generation has a number of offspring whose distribution has generating function g.s/. The next generation has generating function f , the next has g, and the distributions continue to alternate in this way from generation to generation.

(a) Determine the extinction probability of the process in terms of f .s/

and g.s/.

(b) Determine the mean population size at generation n.

(c) Would any of these quantities change if the process started with the g.s/

process and then continued to alternate?