3
\includegraphics[max width=\textwidth, alt={}, center]{c4adc528-ae3f-4ea7-9420-d3e1068a85fe-2_524_796_1105_623}
The continuous random variable \(X\) has probability density function given by
$$f ( x ) = \begin{cases} a x & 0 < x \leqslant 1
b ( 2 - x ) ^ { 2 } & 1 < x \leqslant 2
0 & \text { otherwise } \end{cases}$$
where \(a\) and \(b\) are constants. The graph is shown in the above diagram.
- Find the values of \(a\) and \(b\).
- Find the value of \(\mathrm { E } \left( \frac { 1 } { X } \right)\).