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Math Help - Transformation Technique??

  1. #1
    Yan
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    Transformation Technique??

    If X has a uniform density with α=0 and β=1, show that the random variable Y=-2lnX has a gamma distribution. What are its parameters?
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  2. #2
    Flow Master
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    Quote Originally Posted by Yan View Post
    If X has a uniform density with α=0 and β=1, show that the random variable Y=-2lnX has a gamma distribution. What are its parameters?
    Here is a start:

    The cdf is F(y) = \Pr(-2 \ln X < y) = \Pr \left( \ln X > - \frac{y}{2} \right) = \Pr \left(X > e^{-y/2} \right) = 1 - \Pr \left(X < e^{-y/2} \right) for 0 < y < +\infty and zero otherwise.
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