Question: Given the probability density function

\[f\left( x \right)=\left\{ \begin{aligned} & \frac{1}{20}{{x}^{3}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\le x\le 3 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right.\]

(a) Find the mean

(b) Find \(p\left( 1.3\le x\le 2.6 \right)\)