2 The continuous random variable \(X\) has cumulative distribution function given by $$\mathrm { F } ( x ) = \left\{ \begin{array} { l r } 0 & x < - k
\frac { x + k } { 4 k } & - k \leqslant x \leqslant 3 k
1 & x > 3 k \end{array} \right.$$ where \(k\) is a positive constant.

1. Specify fully, in terms of \(k\), the probability density function of \(X\)
2. Write down, in terms of \(k\), the value of \(\mathrm { E } ( X )\)
3. Show that \(\operatorname { Var } ( X ) = \frac { 4 } { 3 } k ^ { 2 }\)
4. Find, in terms of \(k\), the value of \(\mathrm { E } \left( 3 X ^ { 2 } \right)\)