Case 1: I have two independent exponentially distributed random variables $X$ and $Y$. Intuitively, it makes sense that the sum of those variables is essentially exponentially distributed, but is that correct?
Case 2: I have a uniform random variable $X$ in $(0.75, 1.25)$ (i.e. with mean 1) and an independent exponential random variable $Y$ with parameter $m$. Intuitively, it makes sense that the ratio $\frac{Y}{X}$ is essentially exponentially distributed, but is that correct?