Question: I need help with the following problem: Problem 1. Branching process (10 pts) We consider a branching process (Zn)nEN where the offspring distribution is given

I need help with the following problem:

Problem 1. Branching process (10 pts) We consider a branching process (Zn)nEN where the offspring distribution is given by the prob- ability vector a = (1 - p, 0, p) (i.e. each individual can have either 0 or 2 offspring). (a) Determine P(Z2 = 0) as a function of p. (b) Determine the extinction probability as a function of p. (c) Determine the transition matrix P = (puj)ijEN of the Markov chain (Zn)nEN

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