The continuous random variable \(X\) has probability density function \(f\) given by
\(f(x)=\left\{\begin{array}{ll} a+\frac{1}{5} x & 0 \leqslant x\lt 1 \\ 2 a-\frac{1}{5} x & 1 \leqslant x \leqslant 2 \\ 0 & \text { otherwise } \end{array}\right.\)
where \(a\) is a constant.
(a) Find the value of \(a\).

(b) Find \(\mathrm{E}\left(X^{2}\right)\).

(c) Find the cumulative distribution function of \(X\).