The continuous random variable \(X\) has probability density function \(f\) given by
\(\mathrm{f}(x)=\left\{\begin{array}{ll} k x(4-x) & 0 \leqslant x\lt 2 \\ k(6-x) & 2 \leqslant x \leqslant 6 \\ 0 & \text { otherwise } \end{array}\right.\)
where \(k\) is a constant.
(a) Show that \(k=\frac{3}{40}\).

(b) Given that \(\mathrm{E}(X)=2.5\), find \(\operatorname{Var}(X)\).

(c) Find the median value of \(X\).