4 A continuous random variable \(X\) has probability density function defined by
$$f ( x ) = \begin{cases} k x ^ { 2 } & 0 \leqslant x \leqslant 3
9 k & 3 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
- Sketch the graph of f.
- Show that the value of \(k\) is \(\frac { 1 } { 18 }\).
- Write down the median value of \(X\).
- Calculate the value of the lower quartile of \(X\).