5 The random variable \(X\) has probability density function, f, given by
$$f ( x ) = \begin{cases} \frac { 1 } { x ^ { 2 } } & a < x < b
0 & \text { otherwise } \end{cases}$$
where \(a\) and \(b\) are positive constants.
- It is given that \(\mathrm { E } ( X ) = \ln 2\).
Show that \(b = 2 a\).
- Show that \(a = \frac { 1 } { 2 }\).
- Find the median of \(X\).