Question: Determine whether the given function is a probability density function

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