5. Let 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 39E
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5. Let 0 <p< 1. Consider a branching process with two types of individuals: type A and type
B. Each typc A individual has exactly two offsprings. The typc of cach offspring is chosen
randomly and independently of all the other choices: it will be of type A with probability p
and of type B with probability 1- p. Type B individuals have no offsprings. Suppose that
the process starts with a single type A individual. Find the probability that this population
eventually goes extinct.
Hint: Consider the proccss of just onc of the types.
Transcribed Image Text:5. Let 0 <p< 1. Consider a branching process with two types of individuals: type A and type B. Each typc A individual has exactly two offsprings. The typc of cach offspring is chosen randomly and independently of all the other choices: it will be of type A with probability p and of type B with probability 1- p. Type B individuals have no offsprings. Suppose that the process starts with a single type A individual. Find the probability that this population eventually goes extinct. Hint: Consider the proccss of just onc of the types.
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