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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Originally Posted by Yan 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 $\displaystyle F(y) = \Pr(-2 \ln X < y) = \Pr \left( \ln X > - \frac{y}{2} \right) = \Pr \left(X > e^{-y/2} \right) = 1 - \Pr \left(X < e^{-y/2} \right)$ for $\displaystyle 0 < y < +\infty$ and zero otherwise.
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