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.
- Show that \(k = \frac { 1 } { \ln 3 }\).
- Show that \(\mathrm { E } ( X ) = 3.64\), correct to 3 significant figures.
- Given that the median of \(X\) is \(m\), find \(\mathrm { P } ( m < X < \mathrm { E } ( X ) )\).