Consider randomly selecting a point $\left(X_{1}, X_{2}, X_{3}\right)$ in the unit cube $\left\{\left(x_{1}, x_{2}, x_{3}\right) : 0<x_{1}<1\right.$

$f\left(x_{1}, x_{2}, x_{3}\right)=\left\{\begin{array}{cc}{8 x_{1} x_{2} x_{3}} & {0<x_{1}<1, \quad 0<x_{2}<1, \quad 0<x_{3}<1} \\ {0} & {\text { otherwise }}\end{array}\right.$

(so the three variables are independent). Then form a rectangular solid whose vertices are $(0,0,$

0), $\left(x_{1}, 0,0\right),\left(0, X_{2}, 0\right),\left(X_{1}, X_{2}, 0\right),\left(0,0, X_{3}\right),\left(X_{1}, 0, X_{3}\right),\left(0, X_{2}, X_{3}\right),$ and $\left(X_{1}, X_{2}, X_{3}\right) .$ The

$Y_{2}=X_{1} X_{2} \cdot ]$