3 problems

Let $X_1,\ldots,X_n$ be iid random variables supported on $[0,1]$, with mean $m$, and let an extremal distribution mean one attaining … A distribution is binary if it has two suppo…

Let $X_1,\ldots,X_n$ be iid random variables supported on $[0,1]$, with mean $m$ satisfying $0<m<1$, and write $S_n=X_1+\cdots+X_n$. Define … For $n\geq2$ and $0\leq t<mn$, call a…

Two-error-size conjecture. For each $m$ and $t$, there is an extremal population with just two error sizes, one of which is $0$ or $1$.