Question: 11.1 For a branching process, what is the probability that X(t)=0 eventually? (Population dies out). Show the following: For m < 1, P(Population dies out)=1.

11.1 For a branching process, what is the probability that X(t)=0 eventually?

(Population dies out). Show the following:

For m < 1, P(Population dies out)=1.

If m = 1, then P(Population dies out)=1 except when the number of offspring is exactly 1.

If m > 1? P(Population dies out) > 0 Note that these are exactly the same results as in the case of the Galton–Watson process.

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