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

(c) Find \(\operatorname{Var}(X)\).