6 The random variable $X$ has probability density function given by

$$f ( x ) = \begin{cases} k x ^ { - 1 } & 2 \leqslant x \leqslant 6 \\ 0 & \text { otherwise } \end{cases}$$

where $k$ is a constant.\\
(i) Show that $k = \frac { 1 } { \ln 3 }$.\\

(ii) Show that $\mathrm { E } ( X ) = 3.64$, correct to 3 significant figures.\\

(iii) Given that the median of $X$ is $m$, find $\mathrm { P } ( m < X < \mathrm { E } ( X ) )$.\\

\hfill \mbox{\textit{CAIE S2 2018 Q6}}