The continuous random variable \(T\) follows a rectangular distribution with probability density function given by
$$\mathrm { f } ( t ) = \left\{ \begin{array} { l c }
k & - a \leqslant t \leqslant b
0 & \text { otherwise }
\end{array} \right.$$
Express \(k\) in terms of \(a\) and \(b\).
Prove, using integration, that \(\mathrm { E } ( T ) = \frac { 1 } { 2 } ( b - a )\).
The error, in minutes, made by a commuter when estimating the journey time by train into London may be modelled by the random variable \(T\) with probability density function
$$\mathrm { f } ( t ) = \left\{ \begin{array} { c c }
\frac { 1 } { 10 } & - 4 \leqslant t \leqslant 6
0 & \text { otherwise }
\end{array} \right.$$
Write down the value of \(\mathrm { E } ( T )\).
Calculate \(\mathrm { P } ( T < - 3\) or \(T > 3 )\).