3 problems

Let $X$ and $Y$ be independent non-centered normal random variables, and let $W=XY$. A second-order Stein operator for $W$ is a differential operator acting on smooth functions wit…

Inverse-chi-square conjecture. Then

Let $X$ have density … where $c>0$ is known and the parameter space is $\mathbb{R}\setminus\{0\}$. Pinelis's completeness conjecture. The statistic $X$ is complete. For the paramet…