The question regards Galton-Watson branching process 1. Suggest a random phenomenon which the Galton-Watson branching process might provide a reasonable model. Be clear about the random variable being counted (Zn) and the interpretation of the notion of a 'generation'. 2. The offspring random variable in a Galton Watson branching proces: with a single ancestor in generation 0 has probability generating function II(s) = = 5 - 2s 10 - 7s Find the probability generating function of Z2, the number of individuals in the second generation, and by reference to the Handbook, identify the probability distribution of Z2. Calculate each of the following probabilities correct to four decimal places. (1) The probability of extinction by the third generation. (2) The probability of extinction at the fourth generation. Find the probability that the process will eventually become extinct. Do not use an iterative method to find this probability.
The question regards Galton-Watson branching process 1. Suggest a random phenomenon which the Galton-Watson branching process might provide a reasonable model. Be clear about the random variable being counted (Zn) and the interpretation of the notion of a 'generation'. 2. The offspring random variable in a Galton Watson branching proces: with a single ancestor in generation 0 has probability generating function II(s) = = 5 - 2s 10 - 7s Find the probability generating function of Z2, the number of individuals in the second generation, and by reference to the Handbook, identify the probability distribution of Z2. Calculate each of the following probabilities correct to four decimal places. (1) The probability of extinction by the third generation. (2) The probability of extinction at the fourth generation. Find the probability that the process will eventually become extinct. Do not use an iterative method to find this probability.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The question regards Galton-Watson branching process
1.
Suggest a random phenomenon which the Galton-Watson branching process might
provide a reasonable model. Be clear about the random variable being
counted (Zn) and the interpretation of the notion of a 'generation'.
2.
The offspring random variable in a Galton Watson branching proces:
with a single ancestor in generation 0 has probability generating
function
II(s) =
=
5 - 2s
10 - 7s
Find the probability generating function of Z2, the number of
individuals in the second generation, and by reference to the
Handbook, identify the probability distribution of Z2.
Calculate each of the following probabilities correct to four decimal
places.
(1) The probability of extinction by the third generation.
(2) The probability of extinction at the fourth generation.
Find the probability that the process will eventually become
extinct. Do not use an iterative method to find this probability.
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