The continuous random variable \(X\) has probability density function f given by
\[f(x)=\left\{\begin{array}{ll}
\frac{3}{4 x^{2}}+\frac{1}{4} & 1 \leqslant x \leqslant 3 \\
0 & \text { otherwise }
\end{array}\right.\]
(i) Find the distribution function of \(X\).
(ii) Find the exact value of the interquartile range of \(X\).