Question 9 Let (Xn)nero be a branching process defined as in (8.1.1) in the script on page 310 which satisfies all the following: . Xo = 1, . One has limn-+ E[Xx] = co. Then its extinction probability is equal to zero. YES NO8 Branching Processes Branching processes are used as a tool for modeling in genetics, biomolecular reproduction, population growth, genealogy, disease spread, photomultiplier cascades, nuclear ssion, earthquake triggering, queueing models, viral phenomena, social networks, neuroscience, etc. This chapter mainly deals with the computation of probabilities of matinction and explosion in nite time for branching processes. 3.1 Construction and Examples 3.2 Probability Generating Motions 8.3 Extinction Probabilities Exercises ................................................................ 8.1 Construction and Examples Consider a time-dependent population made of a number X\" of individuals at generation I: 2 0. In the branching process model. each of these X ,1 individuals may have a random number of descendants born at time n. -|- 1. For each is = 1, 2, . . . , X" we let Yg denote the number of descendants of individual 11' k. That means, we have X9 = 1, X1 = Y1, and at time n + 1, the new population size Kn.\" will be given by Kn Xn+1=Yi+"-+Yx,,= Z: Ya. (8.1.1) k-I where the (16,)1 form a. sequence of independent, identically distributed, nonnegative integer valued random variables which are assumed to be almost surely nite, ale. P(Yk