Consider a branching process whose family sizes have the geometric mass function f(k)= qpk, k≥ 0, where p + q = 1, and let Zn be the size of the nth generation. Let T = min {n: Zn = 0} be the extinction time, and suppose that Zo = 1. Find P(T = n). For what values of p is it the case that E(T) <∞o?

Consider a branching process whose family sizes have the geometric mass function f(k)= qpk, k≥ 0, where p + q = 1, and let Zn be the size of the nth generation. Let T = min {n: Zn = 0} be the extinction time, and suppose that Zo = 1. Find P(T = n). For what values of p is it the case that E(T) <∞o?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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