The continuous random variable \(X\) has cumulative distribution function F given by
\(F(x)=\left\{\begin{array}{ll} 0 & x\lt 0, \\ 1-\frac{1}{144}(12-x)^{2} & 0 \leqslant x \leqslant 12, \\ 1 & x\gt 12 . \end{array}\right.\)
(a) Find the upper quartile of \(X\).

(b) Find \(\operatorname{Var}\left(X^{2}\right)\).

The random variable \(Y\) is given by \(Y=\sqrt{X}\).
(c) Find the probability density function of \(Y\).