Question: Let X be a continuous random variable with density function

\[f\left( x \right)=\left\{ \begin{aligned} & \,\,\frac{1}{3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0<x\le 1 \\ & \,\,\frac{5-x}{12}\,\,\,\,\,\,\,\,\,\,\,\,\,1<x<5 \\ & \\ & \,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right.\]

(a) Find \(\Pr \left( 1/2<X<3 \right)\)

(b) Find \(\Pr \left( 2<X<6 \right)\)

(c) Find \(E\left( X \right)\)

(d) Find the first quartile Q₁.

(e) Find the third quartile Q₃