2 A continuous random variable X has the cumulative distribution function:
for € < 0 S e-2 for € > 0.
F(c) =
a) Derive the probability density function of X, i.e f(e).
(2 marks)
(b) Determine the median of X to four decimal places:
3 marks)
(c) State the expected value of X and the variance of X_
(2 marks)
d) Calculate P(X > 4|X > 2) to four decimal places:
marks) (e) Briefly explain whether the distribution is symmetric, positively skewed or negatively skewed: (2 marks)