4 The random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 1 } { 21 } ( x - 1 ) ^ { 2 } & 2 \leqslant x \leqslant 5
0 & \text { otherwise } \end{cases}$$

1. Find the cumulative distribution function of \(X\).
   The random variable \(Y\) is defined by \(Y = ( X - 1 ) ^ { 4 }\).
2. Find the probability density function of \(Y\).
   \includegraphics[max width=\textwidth, alt={}, center]{b9cbf607-4f40-41bb-8374-6b2c39f945ac-09_2725_35_99_20}
3. Find the median value of \(Y\).
4. Find \(\mathrm { E } ( Y )\).