# Exponential and Uniform distributions

• Jan 23rd 2011, 10:42 AM
morganfor
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!
• Jan 23rd 2011, 10:49 AM
CaptainBlack
Quote:

Originally Posted by morganfor
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
• Jan 27th 2011, 05:34 PM
matheagle
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.