6 The continuous random variable \(X\) has the following probability density function:
$$f ( x ) = \begin{cases} a + b x & 0 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
where \(a\) and \(b\) are constants.
- Show that \(2 a + 2 b = 1\).
- It is given that \(\mathrm { E } ( X ) = \frac { 11 } { 9 }\). Use this information to find a second equation connecting \(a\) and \(b\), and hence find the values of \(a\) and \(b\).
- Determine whether the median of \(X\) is greater than, less than, or equal to \(\mathrm { E } ( X )\).