1. A random variable \(X\) has probability density function given by

$$f ( x ) = \left\{ \begin{array} { c c } 0.8 - 6.4 x ^ { - 3 } & 2 \leqslant x \leqslant 4
0 & \text { otherwise } \end{array} \right.$$ The median of \(X\) is \(m\)

1. Show that \(m ^ { 3 } - 3.625 m ^ { 2 } + 4 = 0\)
2. 1. Find \(\mathrm { f } ^ { \prime } ( x )\)
   2. Explain why the mode of \(X\) is 4 Given that \(\mathrm { E } \left( X ^ { 2 } \right) = 10.5\) to 3 significant figures,
3. find \(\operatorname { Var } ( X )\), showing your working clearly.