The random variable \(X\) has probability density function f given by
\(f(x)=\left\{\begin{array}{ll} \frac{1}{21}(x-1)^{2} & 2 \leqslant x \leqslant 5 \\ 0 & \text { otherwise } \end{array}\right.\)
(a) Find the cumulative distribution function of \(X\).

The random variable \(Y\) is defined by \(Y=(X-1)^{4}\).
(b) Find the probability density function of \(Y\).

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

(d) Find \(\mathrm{E}(Y)\).