The continuous random variable \(X\) has probability density function f given by
\(f(x)=\left\{\begin{array}{ll} \frac{1}{6}\left(x^{-\frac{1}{3}}-x^{-\frac{2}{3}}\right) & 1 \leqslant x \leqslant 27 \\ 0 & \text { otherwise } \end{array}\right.\)
(a) Find the cumulative distribution function of \(X\).

The random variable \(Y\) is defined by \(Y=X^{\frac{1}{3}}\).
(b) Find the probability density function of \(Y\).

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