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Branching process, inductive proof

  1. Apr 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Assume that the the offspring distribution is [itex]P(Y=y)=\left(\frac{1}{2}\right)^y\frac{1}{3}[/itex]

    Show by induction that:


    2. The attempt at a solution

    I can see that the distribution is geometric so:


    I assume I have to show that:




    The thing is, this seems like kind of a tedious question considering the amount of marks I'll get for it on my exam. Am I missing something here? Is there a "quick" way to do this?
  2. jcsd
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