=+4. Continuing Example 9.2.5, let P(s) be the generating function for the total number of carrier and normal children born to a carrier of the mutant gene. Express the progeny generating function Q(s) of the mutant-gene branching process in terms of P(s). Find the mean

μ and variance σ2 of Q(s) in terms of the mean α and variance β2 of P(s). How small must α be in order for extinction of the mutant-gene process to be certain?

236 9. Branching Processes