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Thread: Poisson process: phone calls

  1. #1
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    Poisson process: phone calls

    We assume that phone calls arrive according to a Poisson process with rate 2. If I know that up to time t = 1 there is one call only, how likely is it that it arrived after t = 0.75? If I know that up to time t = 1 two calls arrived, how likely is it that the second arrived after t = 0.75?

    So for the first problem I set that
    P(S1>0.75/X(1)=1), with S1, the time it takes for the first event to occur, and X(1), the number of events that occurred up to time 1. But then I don't quite see how to handle it.

  2. #2
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    staassis's Avatar
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    Re: Poisson process: phone calls

    Write the formula for conditional probability and then use the fact that increments of a Poisson process on non-overlapping intervals are independent.

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