The continuous random variable \(X\) has probability density function f given by
\(f(x)=\left\{\begin{array}{cc} \frac{x}{4}\left(4-x^{2}\right) & 0 \leqslant x \leqslant 2 \\ 0 & \text { otherwise } \end{array}\right.\)
(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 \(Y\).