Say we observe the CDF $F_X(x)$ of the random variable $X$. Is it possible to tell whether $X$ can be deconvoluted as $X = Y + e$, where $e$ is a random variable with a standard exponential distribution $exp(1)$ (and where $e$ and $Y$ are independent)?
I can think of necessary conditions for such a deconvolution to exist. For example, I think it must be the case that $F_X(x)$ is continuous. Are there sufficient conditions?
