Question: Given the function

\[f\left( x \right)=\left\{ \begin{aligned} & \frac{3}{28}{{x}^{2}}\,\,\,\,\,\text{if }-3\le x\le 1 \\ & 0\text{ otherwise} \\ \end{aligned} \right.\]

(a) Show that this function is a valid probability density.

(b) Find \(p\left( -2\le x\le 0 \right)\)

(c) Find the mean.