2 problems

Eitan's conjecture. When $p$ and $q$ are even integers, this maximum is attained at $s=0$ or $s=1$, corresponding to a one-sided exponential.

Let $\Gamma$ have density $e^{-(x+1)}\mathbf{1}_{[-1,\infty)}$, let $\Gamma'$ be an independent copy of $\Gamma$, and for $0\leq s\leq 1$ define … For $p\geq q\geq 1$, consider the…