Generation of a branching process

Reference no: EM13985347

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)).

Reference no: EM13985347

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