A continuous random variable \(X\) has cumulative distribution function \(F\) given by

\(F(x)=\begin{cases}0, & x\lt 1,\\ \frac{1}{5}x+a, & 1\leqslant x\lt 4,\\ \frac{1}{50}x^2+b, & 4\leqslant x\leqslant 6,\\ 1, & x\gt 6,\end{cases}\)

where \(a\) and \(b\) are constants.

(a) Find the value of \(a\) and the value of \(b\).

(b) Find the probability density function of \(X\).

(c) Given that \(\mathrm{E}(X)=\frac{529}{150}\), find \(\operatorname{Var}(X)\).

(d) Find the 10th and 90th percentiles of \(X\).