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Math Help - Poisson Process with condition

  1. #1
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    Poisson Process with condition

    People arrive with poisson process with Rate 2

    Find

    (C) P( N(1) = 2 Given N(3) = 6)

    For this i Said this was equal to N(2) = 4 and worked it out using formula.

    (D) This one is driving me crazy.

    P N(1) (Greater than or =) 2 Given N(1) (Greater than or =) 1

    Help With D and confirmation on C would be greatly appreciaded. Thanks!
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Niall101 View Post
    People arrive with poisson process with Rate 2

    Find

    (C) P( N(1) = 2 Given N(3) = 6)

    For this i Said this was equal to N(2) = 4 and worked it out using formula.

    (D) This one is driving me crazy.

    P N(1) (Greater than or =) 2 Given N(1) (Greater than or =) 1

    Help With D and confirmation on C would be greatly appreciaded. Thanks!

    (d) should be {P(N(1)\ge 2)\over P(N(1)\ge 1)}
    Last edited by matheagle; November 1st 2009 at 08:23 PM.
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    Thanks for your reply. Why is this so?
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  4. #4
    MHF Contributor matheagle's Avatar
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    I thought you wanted

    P(N(1)\ge 2)|N(1)\ge 1)

    ={P(N(1)\ge 2,N(1)\ge 1)\over P(N(1)\ge 1)}

    ={P(N(1)\ge 2)\over P(N(1)\ge 1)}
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  5. #5
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    No it is what i wanted, Just wanted to understand where it came from so I can do similar type question myself in the future. Thanks very much for your replies. Really appreciate it.
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