2 The continuous random variable \(X\) has cumulative distribution function F given by
$$F ( x ) = \left\{ \begin{array} { l c }
0 & x < - 1
\frac { 1 } { 2 } ( 1 + x ) ^ { 2 } & - 1 \leqslant x \leqslant 0
1 - \frac { 1 } { 2 } ( 1 - x ) ^ { 2 } & 0 < x \leqslant 1
1 & x > 1
\end{array} \right.$$
- Find the probability density function of \(X\).
- Find \(\mathrm { P } \left( - \frac { 1 } { 2 } \leqslant X \leqslant \frac { 1 } { 2 } \right)\).
- Find \(\mathrm { E } \left( X ^ { 2 } \right)\).
- Find \(\operatorname { Var } \left( X ^ { 2 } \right)\).