6. The continuous random variable \(X\) has the following probability density function: $$f ( x ) = \begin{cases} \frac { 1 } { 6 } x , & 0 \leq x \leq 2
\frac { 1 } { 12 } ( 6 - x ) , & 2 \leq x \leq 6
0 , & \text { otherwise } \end{cases}$$

1. Sketch \(\mathrm { f } ( x )\) for all values of \(x\).
2. State the mode of \(X\).
3. Define fully the cumulative distribution function \(\mathrm { F } ( x )\) of \(X\).
4. Show that the median of \(X\) is 2.536, correct to 4 significant figures.