5 A random variable \(X\) has probability density function given by
$$\mathrm { f } ( x ) = \begin{cases} \frac { k } { x ^ { 3 } } & x \geqslant 1
0 & \text { otherwise } \end{cases}$$
where \(k\) is a constant.
- Show that \(k = 2\).
- Find \(\mathrm { P } ( 1 \leqslant X \leqslant 2 )\).
- Find \(\mathrm { E } ( X )\).