7 The continuous random variable $X$ has probability density function f given by

$$f ( x ) = \left\{ \begin{array} { c c } 
\frac { x } { 4 } \left( 4 - x ^ { 2 } \right) & 0 \leqslant x \leqslant 2 \\
0 & \text { otherwise }
\end{array} \right.$$

(a) Find $\operatorname { Var } ( \sqrt { X } )$.\\

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

(c) Find the exact value of the median of $Y$.\\

If you use the following page to complete the answer to any question, the question number must be clearly shown.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2024 Q7}}