- A continuous random variable \(X\) has probability density function
$$f ( x ) = \left\{ \begin{array} { c l }
a x ^ { - 2 } - b x ^ { - 3 } & 2 \leqslant x < \infty
0 & \text { otherwise }
\end{array} \right.$$
where \(a\) and \(b\) are constants.
Given that \(\mathrm { P } ( X \leqslant 4 ) = \frac { 3 } { 8 }\)
- use algebraic integration to show that \(a = 3\)
Show your working clearly.
- Find the exact value of the median of \(X\)