Given a distribution function $f_X$, where $X$ is some random variable. I want to get the distribution functions of $|X|$ and $\lceil X \rceil$( the last one may only have an easy form if $X$ is exponentially distributed, so it would be sufficient to understand how to construct this function if X is exponentially distributed).
The problem is that I do not see how to construct this distribution function.
Any kind of help is highly appreciated.
Hint:
$\lceil X\rceil\geq k\iff X>k-1$ so: $$P\left\{ \lceil X\rceil\geq k\right\} =P\left\{ X>k-1\right\} $$