Branching process

timer Asked: Apr 1st, 2016

Question description

  1. Consider the following variation of the branching process. At each time n, each individual produces offspring independently using offspring distribution {pk}, and then the individual dies with probability q ∈ (0,1). Hence, each individual reproduces j times where j is the lifetime of the individual. For which values of q, {pk} do we have eventual extinction with a probability of one? (Hint: the answer is quite “clean,” at the end it should relate a common statistic of {pk} to q. Be clear and show your work.) 

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