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Question: lain what is meant by the term branching process ...

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lain what is meant by the term branching process . (Uxford 1974) e nth generation of a branching process in which eac 6. (b) Let Xn be the size of th has probability generating function G, and assume generating function Gn of Xn satisfies Gni(s) - 1. Show fXn satisfies Gn+1 (s) = Gn(G(s)) forn>that the probabili m variable when ar, B (O, 1), and find GIn explicitly wh ß is the probability generating function of a non-ne (c) Show, that G (s) = I-α (1-s) integer-valued random variable is α n Gis thus ity that Xn = 0, and show that it converges as n → oo to I-α1/(1-p) given. 0 (d) Find the probability Explain why this implies that the probability of ultimate extinction equals 1-uni-n (Cambridge 2001)

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