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Probability Poisson Process and Gamma Distribution

  1. Jun 15, 2010 #1
    1. The problem statement, all variables and given/known data


    3. The attempt at a solution

    Part (a) is no problem, it is simply P(X>10) = 1 - P(X<=10) which requires the use of tabulated cumulative poisson values.

    Part (b) is throwing for a loop. I know that I need to invoke the Gamma distribution since that is what the solution is doing. But I don't really understand why. I think that it is because there is some relationship between a Poisson process and the Gamma distribution, but I am not exactly sure what it is.

    What I do know, is that for Poisson processes, the probability that an event occurs X = x number of times in 't' time depends on the average number of times the Poisson event occurs per unit time. But how can I use this knowledge to solve part (b)?

    Any thoughts?

    Here is the solution if it helps to generate any ideas. I am just not sure why they are using the Gamma distribution.

    Last edited: Jun 16, 2010
  2. jcsd
  3. Jun 16, 2010 #2
    Any thoughts on this one? For some reason, I feel like it would make more sense to use the exponential distribution, but again, I am not really sure why. I still don't see why the fact that it is a poisson process allows me to infer that I can or should be using a gamma distribution?
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