A continuous random variable \(X\) has probability density function f given by
\(f(x)=\left\{\begin{array}{ll} k x & 0 \leqslant x\lt 1 \\ k(8-x) & 1 \leqslant x \leqslant 8 \\ 0 & \text { otherwise } \end{array}\right.\)
where \(k\) is a constant.
(a) Show that \(k=\frac{1}{25}\).

(b) Find the median value of \(X\).

The random variable \(Y\) is defined by \(Y=\sqrt[3]{X}\).
(c) Find the probability density function of \(Y\).