5. The random variable \(X\) has probability function
$$P ( X = x ) = \begin{cases} k x , & x = 1,2,3
k ( x + 1 ) , & x = 4,5 \end{cases}$$
where \(k\) is a constant.
- Find the value of \(k\).
- Find the exact value of \(\mathrm { E } ( X )\).
- Show that, to 3 significant figures, \(\operatorname { Var } ( X ) = 1.47\).
- Find, to 1 decimal place, \(\operatorname { Var } ( 4 - 3 X )\).