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Let Snn01 be a branching process whose offspring dist.pdf

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Let (Sn,n=0,1,) be a branching process whose offspring distribution has probability generating function (pgf) G(z). Assume S0=1, and denote by Gn(z) the pgf of Sn, for n=0,1, Show that Gn(z)= Gn1(G(z)) and that Gn(z)=G(Gn1(z)) for n=1,2, [2].

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Let (Sn,n=0,1,) be a branching process whose offspring distribution has probability generating function (pgf) G(z). Assume S0=1, and denote by Gn(z) the pgf of Sn, for n=0,1, Show that Gn(z)= Gn1(G(z)) and that Gn(z)=G(Gn1(z)) for n=1,2, [2]

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  • 1. Let (Sn,n=0,1,) be a branching process whose offspring distribution has probability generating function (pgf) G(z). Assume S0=1, and denote by Gn(z) the pgf of Sn, for n=0,1, Show that Gn(z)= Gn1(G(z)) and that Gn(z)=G(Gn1(z)) for n=1,2, [2]