6 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 3 } { 28 } \left( e ^ { \frac { 1 } { 2 } x } + 4 e ^ { - \frac { 1 } { 2 } x } \right) & 0 \leqslant x \leqslant 2 \ln 3
0 & \text { otherwise } \end{cases}$$

1. Find the cumulative distribution function of \(X\).
   The random variable \(Y\) is defined by \(Y = e ^ { \frac { 1 } { 2 } ( X ) }\).
2. Find the probability density function of \(Y\).
3. Find the 30th percentile of \(Y\).
4. Find \(\mathrm { E } \left( Y ^ { 4 } \right)\).
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