6 A random variable \(X\) has probability density function given by
$$\mathrm { f } ( x ) = \begin{cases} k \left( 3 x - x ^ { 2 } \right) & 0 \leqslant x \leqslant 3
0 & \text { otherwise } \end{cases}$$
- Show that \(k = \frac { 2 } { 9 }\).
- Find \(\mathrm { P } ( 1 \leqslant X \leqslant 2 )\).
- Find \(\operatorname { Var } ( X )\).