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Math Help - Poisson Process

  1. #1
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    Poisson Process

    Hello. I am doing some problem sets (so I'd be probably asking a lot sorry). But for this one:

    Here is the problem:
    The number of accident occurrences at ramp segments of a metropolitan expressway can be described by the Poisson process. Accident data for 1996 indicate that the mean number of occurrences of accidents is 324 cases for the entrance and exit ramp segments of the main line of an urban expressway. What is the probability that in one week, there will be more than 5 accidents? Assume there are 52 weeks in a year.

    My solution:
    There's so many distribution in the Poisson Process but I decided to stick with Poisson Distribution. Do you think it will be effective or do you think I'm wrong?

    Anyway, so my solution therefore has become:
    v=324/52 =6.23 (mean rate of occurrence, is my logic okay?)

    so

    P(xt<=5) = summation (from 0 to 5) of [(6.23^x)(e^-6.23)/x!]
    P(xt<=5) = 0.409

    Please enlighten me. I am still really confused with all these probability distribution.

    I was also thinking whether to use Erlang or Gamma Distribution but I'm really confused.

    Thank you. Any suggestion is greatly appreciated. (And I'm already apologizing now for probably posting more threads later... I'll try to solve them before I post, though).

    PS: I don't know how to input equation here. Cut and Paste won't work with my Word 2007 D:
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  2. #2
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    Quote Originally Posted by warmsheet View Post
    Hello. I am doing some problem sets (so I'd be probably asking a lot sorry). But for this one:

    Here is the problem:
    The number of accident occurrences at ramp segments of a metropolitan expressway can be described by the Poisson process. Accident data for 1996 indicate that the mean number of occurrences of accidents is 324 cases for the entrance and exit ramp segments of the main line of an urban expressway. What is the probability that in one week, there will be more than 5 accidents? Assume there are 52 weeks in a year.

    My solution:
    There's so many distribution in the Poisson Process but I decided to stick with Poisson Distribution. Do you think it will be effective or do you think I'm wrong? Mr F says: Since the question says use the Poisson distribution (read what I highlighted in red), why are you even asking this?

    Anyway, so my solution therefore has become:
    v=324/52 =6.23 (mean rate of occurrence, is my logic okay?) Mr F says: Yes.

    so

    P(xt<=5) = summation (from 0 to 5) of [(6.23^x)(e^-6.23)/x!]
    P(xt<=5) = 0.409

    Please enlighten me. I am still really confused with all these probability distribution. Mr F says: Looks fine assuming your arithmetic is correct.

    I was also thinking whether to use Erlang or Gamma Distribution but I'm really confused. Mr F says: Why? Does the question ask you to do this?

    Thank you. Any suggestion is greatly appreciated. (And I'm already apologizing now for probably posting more threads later... I'll try to solve them before I post, though).

    PS: I don't know how to input equation here. Cut and Paste won't work with my Word 2007 D:
    ..
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  3. #3
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    Oookay. So I guess I should be relieved.

    It's just that when I'm studying problems on books on exponential distributions and erlang distributions, they mention following poisson process so it made me a little confuse as to what to use.

    But I think I'm okay now. I'm almost about to finish my problem set, too, so I don't think I'd have to worry spamming the forum.

    =)

    Thanks, too.
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