5 The time, in minutes, taken by volunteers to complete a task is modelled by the random variable \(X\) with probability density function given by $$\mathrm { f } ( x ) = \begin{cases} \frac { k } { x ^ { 4 } } & x \geqslant 1
0 & \text { otherwise. } \end{cases}$$

1. Show that \(k = 3\).
2. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).