The continuous random variable \(X\) has cumulative distribution function F given by
\(F(x)=\left\{\begin{array}{ll} 0 & x\lt 0, \\ \frac{1}{60}\left(16 x-x^{2}\right) & 0 \leqslant x \leqslant 6, \\ 1 & x\gt 6 . \end{array}\right.\)
(a) Find the interquartile range of \(X\).

(b) Find \(\mathrm{E}\left(X^{3}\right)\).

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