The continuous random variable \(X\) has cumulative distribution function F given by
\(\mathrm{F}(x)=\left\{\begin{array}{ll} 0 & x\lt 2, \\ \frac{1}{60} x^{2}-\frac{1}{15} & 2 \leqslant x \leqslant 8, \\ 1 & x\gt 8 . \end{array}\right.\)
(a) Find \(\mathrm{P}(3 \leqslant X \leqslant 6)\).
(b) Find \(\mathrm{E}(\sqrt{X})\).

(c) Find \(\operatorname{Var}(\sqrt{X})\).

(d) The random variable \(Y\) is defined by \(Y=X^{3}\). Find the probability density function of \(Y\).