The continuous random variable \(X\) has probability density function f given by
\(f(x)=\left\{\begin{array}{ll} \frac{1}{8} & 0 \leqslant x\lt 1 \\ \frac{1}{28}(8-x) & 1 \leqslant x \leqslant 8 \\ 0 & \text { otherwise } \end{array}\right.\)
(a) Find the cumulative distribution function of \(X\).

(b) Find the value of the constant \(a\) such that \(\mathrm{P}(X \leqslant a)=\frac{5}{7}\).

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