6. The continuous random variable \(X\) has probability density function $$f ( x ) = \left\{ \begin{array} { c c } \frac { 1 + x } { k } , & 1 \leqslant x \leqslant 4
0 , & \text { otherwise } \end{array} \right.$$

1. Show that \(k = \frac { 21 } { 2 }\).
2. Specify fully the cumulative distribution function of \(X\).
3. Calculate \(\mathrm { E } ( X )\).
4. Find the value of the median.
5. Write down the mode.
6. Explain why the distribution is negatively skewed.