9 The continuous random variable \(X\) has probability density function given by
$$f ( x ) = \begin{cases} \frac { 1 } { 20 } \left( 3 - \frac { 1 } { \sqrt { } x } \right) & 1 \leqslant x \leqslant 9
0 & \text { otherwise } \end{cases}$$
The random variable \(Y\) is defined by \(Y = \sqrt { } X\).
- Show that the probability density function of \(Y\) is given by
$$\operatorname { g } ( y ) = \begin{cases} \frac { 1 } { 10 } ( 3 y - 1 ) & 1 \leqslant y \leqslant 3
0 & \text { otherwise } \end{cases}$$ - Find the mean value of \(Y\).