6 The continuous random variable \(X\) has the probability density function given by
$$f ( x ) = \left\{ \begin{array} { c c }
3 x ^ { 2 } & 0 < x \leqslant 1
0 & \text { otherwise }
\end{array} \right.$$
- Determine:
- \(\mathrm { E } \left( \frac { 1 } { X } \right)\);
(3 marks) - \(\operatorname { Var } \left( \frac { 1 } { X } \right)\).
- Hence, or otherwise, find the mean and the variance of \(\left( \frac { 5 + 2 X } { X } \right)\).