8 The continuous random variable \(X\) has probability density function given by
$$\mathrm { f } ( x ) = \begin{cases} k x ^ { - a } & x \geqslant 1
0 & \text { otherwise } \end{cases}$$
where \(k\) and \(a\) are constants and \(a\) is greater than 1 .
- Show that \(k = a - 1\).
- Find the variance of \(X\) in the case \(a = 4\).
- It is given that \(\mathrm { P } ( X < 2 ) = 0.9\). Find the value of \(a\), correct to 3 significant figures.