5 A continuous random variable \(X\) has probability density function given by
$$f ( x ) = \begin{cases} a + \frac { 1 } { 3 } x & 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
where \(a\) is a constant.
- Show that the value of \(a\) is \(\frac { 1 } { 2 }\).
- Find \(\mathrm { P } ( X > 1.8 )\).
- Find \(\mathrm { E } ( X )\).