Question 10
Let (Xn)n∈N0 be a branching process defined as in (8.1.1) in the script on page 310 with X0 = 1. Assume that the corresponding (Yn)n∈N satisfy P(Yn = 0) = c0, P(Yn = 1) = c1, for strictly positive constants c0, c1 > 0 satisfying c0 + c1 = 1. Then the extinction probability of the branching process is equal to 1.
(8.1.1): For each k = 1, 2, . . . , Xn we let Yk denote the number of descendants of individual no k. That means, we have X0 = 1, X1 = Y1, and at time n + 1, the new population size Xn+1 will be given by Xn+1 = Y1 + · · · + YXn = summation of Yk from k=1 to Xn
YES or NO
Let (Xn)n∈N0 be a branching process defined as in (8.1.1) in the script on page 310 with X0 = 1. Assume that the corresponding (Yn)n∈N satisfy P(Yn = 0) = c0, P(Yn = 1) = c1, for strictly positive constants c0, c1 > 0 satisfying c0 + c1 = 1. Then the extinction probability of the branching process is equal to 1.
(8.1.1): For each k = 1, 2, . . . , Xn we let Yk denote the number of descendants of individual no k. That means, we have X0 = 1, X1 = Y1, and at time n + 1, the new population size Xn+1 will be given by Xn+1 = Y1 + · · · + YXn = summation of Yk from k=1 to Xn
YES or NO
