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