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?