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A1. (i) Let X be a random variable with probability mass function ( pmf ).....Determine the probability generating function of X.(ii) Suppose that the probability generating function of a random variable X is given by....Determine the probability mass function of X. [5 marks](Hint: You may use the formula: P1...A2. Let Zn, n ≥ 0 be a branching process with offspring distribution.....(i) Find the offspring generating function G(s) and the expectation of N. [4 marks]
(ii) Determine the probability generating function of Z2 and write down P(Z2 = 3).
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keywords: pmf, p.m.f., pgf, p.g.f.
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