2 The continuous random variable \(X\) has cumulative distribution function given by
\(F ( x ) = \begin{cases} 0 & x < a ,
\frac { x - a } { b - a } & a \leqslant x \leqslant b ,
1 & x > b , \end{cases}\)
where \(a\) and \(b\) are constants with \(0 < \mathrm { a } < \mathrm { b }\).

1. Find \(\mathrm { P } \left( \mathrm { X } < \frac { 1 } { 2 } ( \mathrm { a } + \mathrm { b } ) \right)\).
2. Sketch the graph of the probability density function of \(X\).
3. Find the variance of \(X\) when \(a = 2\) and \(b = 8\).