We consider a branching process such that each parents has k de- scendants with probability pk where pk = c(2/3)k with c > 0 being some constant. We start with a single parent at the 0-th stage and we let Xn be the population at the n-th stage.

1. Compute c. (Note: I have c= 1/3) 2. Compute GX3 and give a formula for P (X3 = k) for all k. (Note: I have Gx3(s)=(-6s+7)/(15-14s) and struggle with finding P(X3=k) for all k)

3. Give the probability of extinction for the branching process. (Note: I have P(extinction)=1/2)

Please check answers and help for finding formula for P(X3=k) for all k