Consider a branching process which produces no offspring 20% of the time, one offspring 20%of the time, and two offspring 60% of the time. Suppose that you start (generation 0) with two individuals. (a) What is the expected number of individuals in the 4th generation? (b) What is the próbability of dying out in the first generation? (c) What is the probability of ever dying out?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider a branching process which produces no offspring 20% of the time, one offspring
20%of the time, and two offspring 60% of the time. Suppose that you start (generation
0) with two individuals.
(a) What is the expected number of individuals in the 4th generation?
(b) What is the próbability of dying out in the first generation?
(c) What is the probability of ever dying out?
Transcribed Image Text:Consider a branching process which produces no offspring 20% of the time, one offspring 20%of the time, and two offspring 60% of the time. Suppose that you start (generation 0) with two individuals. (a) What is the expected number of individuals in the 4th generation? (b) What is the próbability of dying out in the first generation? (c) What is the probability of ever dying out?
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