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Math Help - Probability question

  1. #1
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    Probability question

    A train bridge is constructed across a wide river. Trains arrive according to a poisson process of rate lambda=3 per day.

    Find the probability that it takes more than 2 days for the 5th train to arrive at the bridge.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ulysses123 View Post
    A train bridge is constructed across a wide river. Trains arrive according to a poisson process of rate lambda=3 per day.

    Find the probability that it takes more than 2 days for the 5th train to arrive at the bridge.
    The number that arrive in a two day period has a Poission distribution with rate 6 per period.

    So now your question is what is the probability of 4 or fewer trains arrive in a two day period.

    CB
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  3. #3
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    in our book we have that the time of the kth arrival is a gamma distribution. I did it by evaluating the gamma distribution P(T(5)>2)=
    1-P(T(5)<=2)=1-(P(T5=0)+P(T5=1)+P(T5=2)

    this however gives me a difference answer to what i get doing it the way you sugested as a poison process with rate 6.
    can anyone else check if the two mwthods give the same answer?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ulysses123 View Post
    in our book we have that the time of the kth arrival is a gamma distribution. I did it by evaluating the gamma distribution P(T(5)>2)=
    1-P(T(5)<=2)=1-(P(T5=0)+P(T5=1)+P(T5=2)

    this however gives me a difference answer to what i get doing it the way you sugested as a poison process with rate 6.
    can anyone else check if the two mwthods give the same answer?
    That will be because you have to compute:

    1-P(T(5)<=2)=1-(P(T5=0)+P(T5=1|T5<>0)+P(T5=2|(T5<>0)&(T5<>1))

    doing the way you suggest.

    CB
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