The continuous random variable \(X\) has probability density function \(f\) given by
\(f(x)=\left\{\begin{array}{ll} \frac{1}{5} x & 0 \leqslant x\lt 2 \\ \frac{2}{15}(5-x) & 2 \leqslant x \leqslant 5 \\ 0 & \text { otherwise } \end{array}\right.\)
(a) Find the cumulative distribution function of \(X\).

(b) Find the median value of \(X\).

(c) Find \(\mathrm{E}\left(X^{2}\right)\).

(d) Find \(\mathrm{P}(1 \leqslant X \leqslant 3)\).