7. The continuous random variable \(X\) has the following probability density function
$$f ( x ) = \begin{cases} a + b x & 0 \leqslant x \leqslant 5
0 & \text { otherwise } \end{cases}$$
where \(a\) and \(b\) are constants.
- Show that \(10 a + 25 b = 2\)
Given that \(\mathrm { E } ( X ) = \frac { 35 } { 12 }\)
- find a second equation in \(a\) and \(b\),
- hence find the value of \(a\) and the value of \(b\).
- Find, to 3 significant figures, the median of \(X\).
- Comment on the skewness. Give a reason for your answer.