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Poisson distribution

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data

    In a Poisson process with intensity λ, let X1 be the time untill the first event and let X2 be the time between the first and the second event. Let Y be the time untill the second event, that is, Y = X1 + X2. Find the density function f(y).

    2. The attempt at a solution

    Probability that no events occur in time y:

    p(0; \lambda X1) = e^{- \lambda t}

    I don't know if this will be helpful at all...
  2. jcsd
  3. Mar 25, 2009 #2
    I'll give you a hint, the holding times (time between two jumps) of a Poisson process are independent and exponential with parameter lambda. You may want to prove this.
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