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Math Help - exponential random variable

  1. #1
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    exponential random variable

    The time between patient's arriving (90 values) is

    1 1 1 1 1 1 (6)
    2 2 2 2 2 2 (6)
    3 3 3 3 3 3 3 (7)
    4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 (18)
    5 5 5 5 5 5 5 5 5 5 5 5 5 (13)
    6 6 6 6 6 6 6 6 6 6 6 6 6 (13)
    7 7 7 7 7 7 7 (7)
    8 8 8 8 8 8 8 8 (8)
    9 9 9 9 9 9 (6)
    10 10 10 10 (4)
    18 (1)

    If X is an exponential random variable with mean \theta=5, compare the probability P(X>2) with the proportion of times that are greater than 2 from the data.

    Thank you!
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  2. #2
    MHF Contributor matheagle's Avatar
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    P(X>2)={1\over 5}\int_2^{\infty}e^{-x/5}dx= e^{-2/5}

    But this is a continous rv so it also equals P(X\ge 2), but your data looks discrete.

    Next you're supposed to count all the times X exceeds 2 in your sample, but one could also look at all the times X exceeds 1.

    This is why it's good to use the \pm .5 in the normal approximation to the binomial.
    Last edited by matheagle; May 17th 2009 at 08:12 AM.
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