7.56. Let (Zn) be a branching process with Zo = 1 and expected family size μ < 1.Let N = 0 Zn be the total number of individuals in the process over all time.Show that1E{N} = 1- μ[Hint: Count one for the initial individual, and re-assess the situation after the firstfamily is born.]

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Answered: 7.56. Let (Zn) be a branching process…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 67E

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7.56. Let (Zn) be a branching process with Zo = 1 and expected family size μ < 1. Let N = 0 Zn be the total number of individuals in the process over all time. Show that 1 E{N} = 1 - μ [Hint: Count one for the initial individual, and re-assess the situation after the first family is born.]