6. The continuous random variable \(X\) has the following probability density function: $$f ( x ) = \begin{cases} \frac { 1 } { 16 } x , & 2 \leq x \leq 6
0 , & \text { otherwise } \end{cases}$$

1. Sketch \(\mathrm { f } ( x )\) for all values of \(x\).
2. Find \(\mathrm { E } ( X )\).
3. Show that \(\operatorname { Var } ( X ) = \frac { 11 } { 9 }\).
4. Define fully the cumulative distribution function \(\mathrm { F } ( x )\) of \(X\).
5. Show that the interquartile range of \(X\) is \(2 ( \sqrt { } 7 - \sqrt { 3 } )\). END