6 The continuous random variable \(X\) has probability density function given by
$$f ( x ) = \begin{cases} \frac { 1 } { 3 } x ( k - x ) & 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
- Show that the value of \(k\) is \(\frac { 32 } { 9 }\).
- Find \(\mathrm { E } ( X )\).
- Is the median less than or greater than 1.5? Justify your answer numerically.