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!
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.