The continuous random variable \(X\) has probability density function f given by
\(\mathrm{f}(x)=\left\{\begin{array}{ll} \frac{3}{28}\left(\mathrm{e}^{\frac{1}{2} x}+4 \mathrm{e}^{-\frac{1}{2} x}\right) & 0 \leqslant x \leqslant 2 \ln 3 \\ 0 & \text { otherwise } \end{array}\right.\)
(a) Find the cumulative distribution function of \(X\).

The random variable \(Y\) is defined by \(Y=\mathrm{e}^{\frac{1}{2}(X)}\).
(b) Find the probability density function of \(Y\).

(c) Find the 30th percentile of \(Y\).

(d) Find \(\mathrm{E}\left(Y^{4}\right)\).