Question: Consider a branching process as defined in 1.55, in which each family has a number of children that follows a shifted geometric distribution: pk D

Consider a branching process as defined in 1.55, in which each family has a number of children that follows a shifted geometric distribution: pk D p.1 p/k for k 0, which counts the number of failures before the first success when success has probability p. Compute the probability that starting from one individual the chain will be absorbed at 0.

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