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JerJason

Given a Poisson process with an average a(alpha) arrivals per unit of time, find the probability there will be no arrivals during a time interval of length,t, namely, the probability that the waiting time between successive arrivals will be at least of length t.

  • one year ago
  • one year ago

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  1. JerJason
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    The answer my book gets is \[e^{-\alpha t}\] but I'm unsure of what formula to use to obtain that answer.

    • one year ago
  2. JerJason
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    I'm thinking maybe gamma distribution: \[f(x)= \frac{ 1 }{ \beta^{\alpha}\Gamma(\alpha) }x^{\alpha -1}e^{-x/\beta}\] for x>0, alpha>0, beta>0

    • one year ago
  3. UnkleRhaukus
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    wouldn't it be a Poisson distribution?

    • one year ago
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