4 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} k x ^ { 3 } & 0 \leqslant x < 1 ,
k ( 5 - x ) & 1 \leqslant x \leqslant 5 ,
0 & \text { otherwise } , \end{cases}$$ where \(k\) is a constant.

1. Sketch the graph of f.
2. Show that \(k = \frac { 4 } { 33 }\).
   \includegraphics[max width=\textwidth, alt={}, center]{e2a45d19-7d48-4aa5-93f9-6ef90f99d7c4-09_2725_35_99_20}
3. Find the cumulative distribution function of \(X\).
4. Find the median value of \(X\).