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.\\
(a) Show that $k = \frac { a } { a - 1 }$.\\

(b) Find $\mathrm { E } ( X )$ in terms of $a$.\\

(c) Find the 60th percentile of $X$ in terms of $a$.\\

If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.\\

\hfill \mbox{\textit{CAIE S2 2020 Q6}}