The continuous random variable \(X\) has cumulative distribution function F given by
\(F(x)=\left\{\begin{array}{ll} 0 & x\lt 2, \\ \frac{(x-2)^{2}}{12} & 2 \leqslant x\lt 4, \\ 1-\frac{(8-x)^{2}}{24} & 4 \leqslant x \leqslant 8, \\ 1 & x\gt 8 . \end{array}\right.\)
(a) Sketch the graph of the probability density function of \(X\).

(b) Find \(\mathrm{E}(X)\).

(c) Find the exact value of the interquartile range of \(X\).