Math Problem Statement
In a branching process, let Hn(t) be the generating function for the total number of individuals up to and including generation n; i.e. Hn(t) = E ( tZ1+···+Zn ) . Find a recursive equation for Hn in terms of t, Hn−1 and GX
Solution
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Math Problem Analysis
Mathematical Concepts
Branching Process
Generating Functions
Probability
Formulas
H_n(t) = E(t^(Z1 + Z2 + ... + Zn))
H_0(t) = t
H_n(t) = H_{n-1}(G_X(t))
Theorems
Generating Function Theorem
Recursive Formulas in Branching Processes
Suitable Grade Level
University Level (Advanced Probability Theory)
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