8 The continuous random variable \(X\) has probability density function f given by
$$f ( x ) = \begin{cases} \frac { 1 } { 4 } ( x - 1 ) & 2 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
- Find the distribution function of \(X\).
The random variable \(Y\) is defined by \(Y = ( X - 1 ) ^ { 3 }\). - Find the probability density function of \(Y\).
- Find the median value of \(Y\).