The continuous random variable \(X\) has distribution function given by
\[\mathrm{F}(x)=\left\{\begin{array}{ll}
0 & x<0, \\
\frac{1}{90}\left(x^{2}+x^{4}\right) & 0 \leqslant x \leqslant 3, \\
1 & x>3 .
\end{array}\right.\]

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

(ii) Find the mean value of \(Y\).