2 problems

Let $X$ and $Y$ be independent positive random variables, and define $U$ and $V$ by the transformation in the preceding independence property. Suppose that $U$ and $V$ are also ind…

Let $X_1,X_2,\ldots,X_n$ be a random sample of size $n\geq 3$ from any distribution $F$ on $\mathbb{R}$. Write $\overline{X}_n$ for the sample mean and $G_n$ for Gini's mean differ…