The continuous random variable \(X\) has probability density function \(f\) given by
\(f(x)=\left\{\begin{array}{ll} \frac{3}{8}\left(1+\frac{1}{x^{2}}\right) & 1 \leqslant x \leqslant 3 \\ 0 & \text { otherwise } \end{array}\right.\)
(a) Find \(\mathrm{E}(\sqrt{X})\).

The random variable \(Y\) is given by \(Y=X^{2}\).
(b) Find the probability density function of \(Y\).

(c) Find the 40th percentile of \(Y\).