7 The continuous random variable \(X\) has probability density function given by
$$f ( x ) = \begin{cases} \frac { 1 } { 21 } x ^ { 2 } & 1 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
The random variable \(Y\) is defined by \(Y = X ^ { 2 }\).
- Show that \(Y\) has probability density function given by
$$g ( y ) = \begin{cases} \frac { 1 } { 42 } y ^ { \frac { 1 } { 2 } } & 1 \leqslant y \leqslant 16
0 & \text { otherwise } \end{cases}$$ - Find the median value of \(Y\).
- Find the expected value of \(Y\).