6 A random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { k } { x ^ { 2 } } & 1 \leqslant x \leqslant a
0 & \text { otherwise } \end{cases}$$ where \(k\) and \(a\) are positive constants.

1. Show that \(k = \frac { a } { a - 1 }\).
2. Find \(\mathrm { E } ( X )\) in terms of \(a\).
3. Find the 60th percentile of \(X\) in terms of \(a\).
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