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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- Jan 23rd 2011, 10:42 AMmorganforExponential 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! - Jan 23rd 2011, 10:49 AMCaptainBlack
- Jan 27th 2011, 05:34 PMmatheagle
First of all.

If X is an exponential, then it's support is on $\displaystyle (0,\infty)$

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

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

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

and make the appropriate substitution.