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Probability distribution of first arrival time in Poisson Process

  1. Jul 28, 2014 #1
    According to wiki:
    http://en.wikipedia.org/wiki/Poisson_process

    The probability for the waiting time to observe first arrival in a Poisson process P(T1>t)=exp(-lambda*t)
    But what is the Probability Distribution P(T1=t) of the waiting time itself? How to calculate that?
     
  2. jcsd
  3. Jul 29, 2014 #2

    mathman

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    Since the waiting time has a continuous distribution, the probability of T1 having a particular value = 0. I suppose you would want the density function, λe-λt.
     
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