7 A continuous random variable \(X\) has probability density function
$$f ( x ) = \left\{ \begin{array} { c c }
a x ^ { - 3 } + b x ^ { - 4 } & x \geqslant 1
0 & \text { otherwise }
\end{array} \right.$$
where \(a\) and \(b\) are constants.
- Explain what the letter \(x\) represents.
It is given that \(\mathrm { P } ( X > 2 ) = \frac { 3 } { 16 }\).
- Show that \(a = 1\), and find the value of \(b\).
- Find \(\mathrm { E } ( X )\).