Let Zn be a branching process with offspring distribution pk with p0 > 0and

 D P

k kpk > 1. Let ./ D P1 kD0 pkk.

(a) Show that E.ZnC1 jZn/ D ./Zn .

(b) Let be the solution <1 of .

/ D and conclude that Pk.T0 < 1/ D k.