Given (X_{0}=1), show that the probability of extinction (pi_{0}) satisfies equation [Mleft(pi_{0} ight)=pi_{0}] by applying the total

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Given $X_{0}=1$, show that the probability of extinction $\pi_{0}$ satisfies equation

\[M\left(\pi_{0}\right)=\pi_{0}\]

by applying the total probability rule (condition with regard to the number of offspring of the individual in the zerouth generation). Make use of the answer to exercise 8.28.

Data from answer of Exercise 8.28

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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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Given (X_{0}=1), show that the probability of extinction (pi_{0}) satisfies equation [Mleft(pi_{0} ight)=pi_{0}] by applying the total

Question:

The offspring of the n individuals generates n independent Galton-Watson processes. Each of them has extinction probability o. Therefore, the extinction probability of a Galton-Watson process starting with n individuals is .

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Applied Probability And Stochastic Processes

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