1. A random variable \(X\) has probability density function given by

$$f ( x ) = \left\{ \begin{array} { c c } \frac { 1 } { 4 } & - \frac { 1 } { 2 } \leqslant x < \frac { 1 } { 2 }
2 x - \frac { 3 } { 4 } & \frac { 1 } { 2 } \leqslant x \leqslant k
0 & \text { otherwise } \end{array} \right.$$ where \(k\) is a positive constant.

1. Sketch the graph of \(\mathrm { f } ( x )\)
2. By forming and solving an equation in \(k\), show that \(k = 1.25\)
3. Use calculus to find \(\mathrm { E } ( X )\)
4. Calculate the interquartile range of \(X\)