Consider a branching process in which each item produces k items with probability 1/4, where 0 ≤ k ≤ 3. First show that the extinction probability z is in the interval [.30, .50]. Then compute the...

Consider a branching process in which each item produces k items with probability 1/4, where 0 ≤ k ≤ 3. First show that the extinction probability z is in the interval [.30, .50]. Then compute the extinction probability of the process by the procedure in Remark 49 for ε = .001. Alternatively, the probability can be obtained – you need not do this – by solving the cubic equation