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Math Help - exponential distribution

  1. #1
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    exponential distribution

    Hi can anybody help me with exponential distribution?

    The speed of wind can be modelled with an exponential distribution with a mean of 40 miles per hour.
    At a random location what is the probability that wind speed is less than 25 miles per hour?
    What is the probability at a random location wind speed will exceed 100 miles an hour?

    Now i know that this can be modelled as lamda e^(-lamda x)
    and i also know that in that equation that lamda can be replaced by 1/40 (i think!) But i'm not sure how to work out the question. Can anybody give me a hand?
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by studentsteve1202 View Post
    Now i know that this can be modelled as lamda e^(-lamda x)
    There is just a \lambda missing : f_X(x)=\lambda\exp(-\lambda x) with x\geq 0.
    and i also know that in that equation that lamda can be replaced by 1/40
    Yes
    But i'm not sure how to work out the question. Can anybody give me a hand?
    Denote V the random variable associated to the wind speed

    The probability that the wind speed is less than V_0 is given by
    P(V\leq V_0)=\int_0^{V_0}\lambda\exp(-\lambda x)\mathrm{d}x

    As the wind speed is either greater than V_0, either less than V_0, P(V\geq V_0)=1-P(V\leq V_0).

    Hope that helps.
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