Let $Z$ be an exponential random variable and $R$ an independent nonnegative random variable. Show that $$ P(Z-R > u | Z > R ) = P(Z > u) $$ From here, I can use Bayes Theorem to split the Left Hand Side, and I know that I have to integrate them.
However, I'm not sure how to exactly to proceed from here. I know that $u \geq 0$.
Any help would be greatly appreciated.
Thanks!