The continuous random variable \(X\) has probability density function f given by
\(\mathrm{f}(x)=\left\{\begin{array}{ll} k x & 0 \leqslant x\lt 1, \\ k x^{2} & 1 \leqslant x \leqslant 2, \\ 0 & \text { otherwise. } \end{array}\right.\)
(a) Show that \(k=\frac{6}{17}\).

(b) Find the cumulative distribution function of \(X\).

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

(d) Find \(\mathrm{E}\left(\frac{1}{X}\right)\).