[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

A die is rolled twice. Let [math]X[/math] denote the sum of the two numbers that turn up, and [math]Y[/math] the difference of the numbers (specifically, the number on the first roll minus the number on the second). Show that [math]E(XY) = E(X)E(Y)[/math]. Are [math]X[/math] and [math]Y[/math] independent?