2 problems

Let $m\geq 2$ be a fixed integer. For independent exponential random variables $Y_k$ with rates $k$, define the limiting maximizing index … where … and write…

Let $q>0$ be real, let $a_1,\dots,a_n$ be non-negative real numbers satisfying … and let $X_1,\dots,X_n$ be independent identically distributed standard exponential random variable…