Consider a branching process in which the number of offspring per individual has a Poisson distribution with mean A, A> 1 Let , denote the probability that, starting with a single individual, the population eventually becomes extinct Also, let

a, a < 1, be such that

(a) Show that a = A. ae = Ae

(b) Show that, conditional on eventual extinction, the branching process follows the same probability law as the branching process in which the number of offspring per individual is Poisson with mean a