7 The continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} k x ^ { 2 } & 0 \leqslant x \leqslant a
0 & \text { otherwise } \end{cases}$$
where \(a\) and \(k\) are constants.
- Sketch the graph of \(y = \mathrm { f } ( x )\) and explain in non-technical language what this tells you about \(X\).
- Given that \(\mathrm { E } ( X ) = 4.5\), find
(a) the value of \(a\),
(b) \(\operatorname { Var } ( X )\).