4 The continuous random variable \(X\) has a probability density function given by $$\mathrm { f } ( x ) = \begin{cases} \frac { 1 } { 2 } k ( x - 1 ) & 1 \leqslant x \leqslant 3
k & 3 < x \leqslant 6
\frac { 1 } { 4 } k ( 10 - x ) & 6 < x \leqslant 10
0 & \text { otherwise } \end{cases}$$ where \(k\) is a positive constant.

1. Sketch \(\mathrm { f } ( x )\) for all values of \(x\)
2. Show that \(k = \frac { 1 } { 6 }\)
3. Specify fully the cumulative distribution function \(\mathrm { F } ( x )\) of \(X\) Given that \(\mathrm { E } ( X ) = \frac { 61 } { 12 }\)
4. find \(\mathrm { P } ( X > \mathrm { E } ( X ) )\)
5. Describe the skewness of the distribution, giving a reason for your answer.