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Write down generating function for offspring distribution

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Let {Zn}n∈N0 be a simple branching process which starts from one individual. Each individual has exactly three children, each of whom survives until reproductive age with probability 0 < p < 1, and dies before he/she is able to reproduce with probability q = 1 - p, independently of his/her siblings. The children that reach reproductive age reproduce according to the same rule.

1. Write down the generating function for the offspring distribution.

2. For what values of p will the population go extinct with probability 1.

(Hint: You don't need to compute much. Just find the derivative P0(1) and remember the picture from class →)1.

Reference no: EM131127755

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