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.
First of all.
If X is an exponential, then it's support is on
If , then Y's support is
and you can't have a uniform distribution on the real line.
Use your CDF of X, or
and make the appropriate substitution.