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Math Help - Poisson distribution.

  1. #1
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    Poisson distribution.

    An insurance company receives on average 3 claims per month from a certain town.Assuming that the number of claims follows a Poisson distribution, find the probability
    a) it receives less than 3 claims in a given month;
    b) it receives more than 2 more in a given three month period

    pls help me solve...
    Last edited by mr fantastic; July 6th 2011 at 02:34 PM. Reason: Re-titled.
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  2. #2
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    Re: Help solve this probability question

    Quote Originally Posted by SLJSWW View Post
    a) it receives less than 3 claims in a given month;
    Make \displaystyle \lambda = 3 and find \displaystyle P(x<3) = P(x=0)+P(x=1)+P(x=2)

    where \displaystyle P(x=k) = \frac{\lambda^k\times e^{-\lambda}}{k!}


    Quote Originally Posted by SLJSWW View Post

    b) it receives more than 2 more in a given three month period
    for a 3 month period make \displaystyle \lambda = 3\times 3 and find \displaystyle P(x>2) = 1-P(x\leq 2)

    where \displaystyle P(x=k) = \frac{\lambda^k\times e^{-\lambda}}{k!}
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