4 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 3 } { 8 } \left( 1 + \frac { 1 } { x ^ { 2 } } \right) & 1 \leqslant x \leqslant 3
0 & \text { otherwise } \end{cases}$$

1. Find \(\mathrm { E } ( \sqrt { X } )\).
   The random variable \(Y\) is given by \(Y = X ^ { 2 }\).
2. Find the probability density function of \(Y\).
3. Find the 40th percentile of \(Y\).