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Math Help - Exponential and Uniform distributions

  1. #1
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    Exponential and Uniform distributions

    I'm stuck on this question:

    If RV X has an exponential distribution does Y = ln(X) have a uniform
    distribution? Derive the cumulative distribution function and density of Y.

    Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by morganfor View Post
    I'm stuck on this question:

    If RV X has an exponential distribution does Y = ln(X) have a uniform
    distribution? Derive the cumulative distribution function and density of Y.

    Thanks!
    No. Using the cumulative distribution function of X find that of Y, you will find that the CDF of Y is not proportional to y.

    CB
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  3. #3
    MHF Contributor matheagle's Avatar
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    First of all.
    If X is an exponential, then it's support is on (0,\infty)

    If Y=\ln X, then Y's support is (-\infty,\infty)

    and you can't have a uniform distribution on the real line.

    Use your CDF of X, 1-e^{-\lambda x} or 1-e^{-x/\lambda}

    and make the appropriate substitution.
    Last edited by matheagle; January 27th 2011 at 09:29 PM.
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