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Math Help - approximations for discrete distributions

  1. #1
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    approximations for discrete distributions

    The number of trees in one acre has a Poisson distribution with mean 60. Assuming independence, compute approximately P(5950 \le X \le 6100), where X is the number of trees in 100 acres.

    Could someone work this problem out for me or a similar one? I have a few of this type to do. Thank you
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  2. #2
    Super Member Random Variable's Avatar
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    The sum of n independent Poisson random variables each with parameter  \lambda_{i} is itself a Poisson random variable with parameter  \sum^{n}_{i=1} \lambda_{i} .

    So X is Poisson random variable with parameter 60*n = 60*100 = 6000. Therefore, X has a mean a 6000 and a variance of 6000.

    Since n is fairly large,  \frac {X-6000}{\sqrt{6000}} is approximately N(0,1) by the central limit theorem

    so find  P(\frac {5950-6000}{\sqrt{6000}} \le Z \le \frac {6100-6000}{\sqrt{6000}})

    If you were dealing with a strict inequality, the answer would be different.
    Last edited by Random Variable; May 30th 2009 at 09:43 AM.
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