In a Galton-Walton branching process, the offspring distribution is given by
Find the probability of extinction (assuming )
find the generating function first G(s).
now to find e so i need to find smallest non negative solution of s=G(s)
and i get:
however the next part of the question asks you to find, supposing has a poisson distribution with mean . Supposing also that the probability of ultimate extinction is
I know that if then it will be
however i cannot see how to get another distribution into the answer