The continuous random variable \(X\) follows a rectangular distribution with probability density function defined by
$$f ( x ) = \begin{cases} \frac { 1 } { b } & 0 \leqslant x \leqslant b 0 & \text { otherwise } \end{cases}$$
Write down \(\mathrm { E } ( X )\).
Prove, using integration, that
$$\operatorname { Var } ( X ) = \frac { 1 } { 12 } b ^ { 2 }$$
At an athletics meeting, the error, in seconds, made in recording the time taken to complete the 10000 metres race may be modelled by the random variable \(T\), having the probability density function
$$f ( t ) = \left\{ \begin{array} { c c }
5 & - 0.1 \leqslant t \leqslant 0.1
0 & \text { otherwise }
\end{array} \right.$$
Calculate \(\mathrm { P } ( | T | > 0.02 )\).