two random variables: most probable cut or break

Question

Let $X$ and $Y$ be (dependent) random variables that are known to satisfy $X < Y$. Consider the function $F(s) = P\{X < s < Y\}$. Under certain circumstances, $F$ is unimodal. Does the maximizing value $s = s_0$ have a standard name? A phrase akin to "most probable cut" or "most likely break" might be applicable, but I wish to be consistent with the literature (if any). References would be welcome and most appreciated.