3 The continuous random variable \(R\) follows a rectangular distribution with probability density function given by $$f ( r ) = \begin{cases} k & - a \leq r \leq b
0 & \text { otherwise } \end{cases}$$ Prove, using integration, that \(\mathrm { E } ( R ) = \frac { 1 } { 2 } ( b - a )\)
[0pt] [4 marks]