7 problems

Let $X_1,\ldots,X_n$ be independent and identically distributed random variables with an analytic density on $(0,\infty)$, and let $X_{(k;n)}$ denote the $k$-th order statistic. Ar…

The setting concerns the argmaximum of observations when the distributions of the $X$'s are not continuous, so that several observations may attain the maximum. Random tie-breaking…

Universal scaling conjecture. Based on numerical simulations, the limiting behaviors in Eqs. and should hold for every continuous and symmetric jump distribution with finite varian…

Uniform-maximization conjecture. As ${\boldsymbol p}$ varies in ${\cal M}_N$, the coefficient of correlation of any two order statistics from ${\cal P}_0({\boldsymbol p})$ is maxim…

Terrell's conjecture. The coefficient $rho_{12}$ is never greater than one-half.

Let $X=\delta+Z$ be a CU service time, where $\delta\ge 0$ is constant and the support of the random variable $Z$ includes $0$. Under server-dependent scaling, consider the expecte…

Consider the simple small-area model with area random effects having distribution $F$ and sampling errors having distribution $G$. Let…