Question: The following is a density function:

\[f\left( x \right)=\left\{ \begin{aligned} & 2x{{e}^{-{{x}^{2}}}}\,\,\,\,\,\,\,\,\,\,\,x\ge 0 \\ & 0\text{ }x<0 \\ \end{aligned} \right.\]

Compute

(a) \(\Pr \left( X\ge 0 \right)\)

(b) \(\Pr \left( 1\le X\le 2 \right)\)

(c) \(\Pr \left( X\le 2 \right)\)