7 The continuous random variable \(X\) has distribution function given by
$$\mathrm { F } ( x ) = \begin{cases} 0 & x < 0 ,
\frac { 1 } { 90 } \left( x ^ { 2 } + x ^ { 4 } \right) & 0 \leqslant x \leqslant 3 ,
1 & x > 3 . \end{cases}$$
The random variable \(Y\) is defined by \(Y = X ^ { 2 }\).
- Find the probability density function of \(Y\).
- Find the mean value of \(Y\).