5 A random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { 3 } { 16 } \left( 4 x - x ^ { 2 } \right) & 2 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$

1. Show that \(\mathrm { E } ( X ) = \frac { 11 } { 4 }\).
2. Find \(\operatorname { Var } ( X )\).
3. Given that the median of \(X\) is \(m\), find \(\mathrm { P } ( m < X < 3 )\).