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

\[M(z)=(0.6 z+0.4)^{3}\]

(1) What type of probability distribution has $Y$ ?

(2) Determine the probabilities $P(Y=k)$.

(3) What is the corresponding probability of extinction?

(4) Let $T$ be the random time to extinction. Determine the probability $P(T=2)$ by applying formula (8.60). Verify this result by applying the total probability rule to $P(T=2)$.

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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

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