The continuous random variable \(X\) has cumulative distribution function F given by
\(F(x)=\left\{\begin{array}{ll} 0 & x\lt 0, \\ \frac{1}{81} x^{2} & 0 \leqslant x \leqslant 9, \\ 1 & x\gt 9 . \end{array}\right.\)
(a) Find \(\mathrm{E}(\sqrt{X})\).

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

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