3 problems

Polynomial tail conjecture. For every $p>{\rm H}(W)$, there exists a constant $C>0$ such that

Let $X$ and $Y$ be independent random variables on $\mathbb{R}_+$ that are not compactly supported, and let $\lambda\in(0,1)$. Weighted-average tail conjecture. … This conjecture i…

Let $m_k(x)$ denote the supremum of $\mathbb{P}(X_1+\cdots+X_k\geq 1)$ over nonnegative, independent and identically distributed random variables with $\mathbb{E}(X_i)\leq x$. For…