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Let X(n) be the number of individuals in the nth generation of a branching process (X(0) = 1), and set Tn = 1 + X(1)+ · · · + X(n), that is, Tn equals the total progeny up to and including generation number n. Let g(t) and Gn(t) be the generating functions of X(1) and Tn, respectively. Prove the following formula: Gn(t) = t · g(Gn-1(t)).

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M91695216

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