The continuous random variable \(X\) has probability density function f given by
\(f(x)=\left\{\begin{array}{ll} k x^{3} & 0 \leqslant x\lt 1 \\ k(5-x) & 1 \leqslant x \leqslant 5 \\ 0 & \text { otherwise } \end{array}\right.\)
where \(k\) is a constant.
(a) Sketch the graph of f.

(b) Show that \(k=\frac{4}{33}\).

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

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