4 The continuous random variable \(X\) has cumulative distribution function F given by $$F ( x ) = \begin{cases} 0 & x < 2
\frac { 1 } { 60 } x ^ { 2 } - \frac { 1 } { 15 } & 2 \leqslant x \leqslant 8
1 & x > 8 \end{cases}$$

1. Find \(\mathrm { P } ( 3 \leqslant X \leqslant 6 )\).
2. Find \(\mathrm { E } ( \sqrt { X } )\).
3. Find \(\operatorname { Var } ( \sqrt { X } )\).
4. The random variable \(Y\) is defined by \(Y = X ^ { 3 }\). Find the probability density function of \(Y\).