10 problems

Optimal-strategy conjecture. After observing $I_{k}=1$, the player whose turn it is should give up his turn to his opponent if and only if $p_{i,k}<\frac{1}{2}$ for all $i>k$. This…

Let $N\ge 3$, and let $l$ and $m$ be positive integers such that $1\le l\le N$, $2\le m\le N-1$, and both $l$ and $m$ are relatively prime to $N$. Let $X_l(m,N)$ be the random vari…

Existence conjecture. Under certain conditions on $W$, there exists a random variable $V$, independent of $W$ and with support in $[0,1]$, such that holds. In terms of…

General CNF–DNF correlation conjecture. Under these assumptions, the inequality referred to in the source as the CNF–DNF inequality holds.

Burdzy–Pitman conjecture. For every $\delta\in(\frac{1}{2},1]$,

Leader–Radcliffe's conjecture.

Let $n \in \mathbb{Z}_{\ge 1}$, let $\mu_1 \ge \dotsc \ge \mu_n > 0$ satisfy … and let $X_1,\dotsc,X_n$ be independent non-negative random variables with $EX_i=1$ for every $i$. De…

Let $n \in \mathbb{Z}_{\ge 1}$, let $\mu_1 \ge \dotsc \ge \mu_n > 0$ satisfy … and let $X_1,\dotsc,X_n$ be independent non-negative random variables with $EX_i=1$ for every $i$. De…

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…

Samuels's conjecture. For all admissible values of $\mu_1,\ldots,\mu_l$,