[See Solution] Determine whether the function is a probability density function, show your work.
Question:
Determine whether the function is a probability density function, show your work.
\[f(x)=\left\{ \begin{matrix} x\,{{e}^{-{{x}^{2}}}}\ for\quad x\ge 0 \\ 0\quad for\quad x<0 \\ \end{matrix} \right.\]
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