A continuous random variable X has the cumulative distribution function: F(x)=\left\{\begin{array}{ll} 0 & \text { for } x<0 \\ 1-\mathrm{e}^{-2 x} & \text { for } x \geq 0 \end{array}\right.

\text { (a) Derive the probability density function of } \boldsymbol{X} \text {, i.e. } \boldsymbol{f}(\boldsymbol{x}) \text {. } (b) Determine the median of X to four decimal places. (c) State the expected value of X and the variance of X. (d) Calculate P(X > 4| X > 2) to four decimal places. (e) Briefly explain whether the distribution is symmetric, positively skewed or negatively skewed.