3 The continuous random variable \(X\) has probability density function f given by
$$f ( x ) = \begin{cases} a + \frac { 1 } { 5 } x & 0 \leqslant x < 1
2 a - \frac { 1 } { 5 } x & 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
where \(a\) is a constant.
- Find the value of \(a\).
- Find \(\mathrm { E } \left( X ^ { 2 } \right)\).
- Find the cumulative distribution function of \(X\).