Given $f(x)=\frac{3}{32}\left(4-x^{2}\right)$ over the interval $[-2,2] .$ (a) Show that $f$ is a $p d f$ and determine (b) $\operatorname{Pr}(1 \leq x \leq 2),(\text { c) } \operatorname{Pr}(-1 \leq x \leq 0), \text { (d) } \operatorname{Pr}(|x| \leq 1),$

(e) $\operatorname{Pr}(x \leq 1),$ (f) $\operatorname{Pr}(x \geq 0).$