[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]

Suppose that [math]R^2 = X^2 + Y^2[/math]. Find [math]f_{R^2}[/math] and [math]f_R[/math] if

[[math]] f_X(x) = f_Y(x) = \left \{ \begin{array}{ll} 1/2, & \mbox{if $-1 \leq x \leq 1,$} \\ 0, & \mbox{otherwise.} \end{array} \right. [[/math]]