[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]

Explain how you can generate a random variable whose

cumulative distribution function is </math> F(x) = \left \{ \begin{array}{ll}

            0, & \mbox{if [math]x  \lt  0[/math]}, \\
          x^2, & \mbox{if [math]0 \leq x \leq 1[/math]}, \\
            1, & \mbox{if [math]x  \gt  1.[/math]}
               \end{array}
      \right.

<math display="block">