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JerJason

  • 3 years ago

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.

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  1. JerJason
    • 3 years ago
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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.

  2. JerJason
    • 3 years ago
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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

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

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