A Galton-Watson process starts with one individual. The random number of offspring (Y) of this individual has

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A Galton-Watson process starts with one individual. The random number of offspring $Y$ of this individual has the $z$-transform

\[M(z)=e^{1.5(z-1)}\]

(1) What is the underlying probability distribution of $Y$ ?

(2) Determine the corresponding probability of extinction.

(3) Let $T$ be the random time to extinction. Determine the probability $P(T=3)$ by applying formula (8.60).

Data from 8.60

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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

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Question Posted: Apr 26, 2024 04:01 PM

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A Galton-Watson process starts with one individual. The random number of offspring (Y) of this individual has

Question:

= P(T n) Mn(0)-Mn-1 (0), n = 1, 2,....

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Applied Probability And Stochastic Processes

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