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Math Help - The Exponential Distribution

  1. #1
    Senior Member chella182's Avatar
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    [SOLVED] The Exponential Distribution

    The question goes as follows...

    Annual wind speed maxia for various hurricane-prone locations in the American Deep South can be modelled with an exponential distribution with mean 58 miles per hour.

    a) Find the probability that, for a randomly chosen location in the Deep South, the annual maximum wind speed is less than 30 miles per hour.

    b) Find the probability that, for one of these locations, the annual maximum wind speed will exceed that observed for New Orleans during Hurricane Katrina of 181 miles per hour.
    For the first part I got an answer of 1 when I initally tried it, which is obviously wrong. Thanks in advance for any help
    Last edited by chella182; April 30th 2009 at 06:10 AM. Reason: Solved it
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  2. #2
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    Quote Originally Posted by chella182 View Post
    The question goes as follows...

    Annual wind speed maxia for various hurricane-prone locations in the American Deep South can be modelled with an exponential distribution with mean 58 miles per hour.

    a) Find the probability that, for a randomly chosen location in the Deep South, the annual maximum wind speed is less than 30 miles per hour.

    b) Find the probability that, for one of these locations, the annual maximum wind speed will exceed that observed for New Orleans during Hurricane Katrina of 181 miles per hour.


    For the first part I got an answer of 1 when I initally tried it, which is obviously wrong. Thanks in advance for any help
    Let the pdf be f(x).

    a) \Pr(X < 30) = \int_0^{30} f(x) \, dx.

    b) \Pr(X > 181) = \int_{181}^{+\infty} f(x) \, dx.
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  3. #3
    Senior Member chella182's Avatar
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    Okay, this is sorted now - one of my friends in the year above me pointed out my silly mistake
    Last edited by chella182; April 30th 2009 at 06:10 AM. Reason: LaTex mess-up
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