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

1. Determine \(\mathrm { P } \left( - \frac { 3 c } { 4 } < X < \frac { 3 c } { 4 } \right)\).
2. Show that the probability density function, \(\mathrm { f } ( x )\), of \(X\) is $$f ( x ) = \left\{ \begin{array} { c c } \frac { 1 } { 4 c } & - c \leqslant x \leqslant 3 c
   0 & \text { otherwise } \end{array} \right.$$
3. Hence, or otherwise, find expressions, in terms of \(c\), for:
   1. \(\mathrm { E } ( X )\);
   2. \(\operatorname { Var } ( X )\).