b) A random variable X has an exponential distribution with mean = 1/2. Find: i. P(X > 3) [1 MARK] ii. P(X > 2) [1 MARK] iii. P(X > 3| X > 2) [3 MARKS] iv. Show that P(X> 1) = P(X > 3| X > 2) [2 MARKS] c) Consider tossing a fair six-sided die once and define events A = {2, 4, 6}, B = {1, 2, 3}, and C = {1, 2, 3, 4}. Calculate the following: i. P(A) [1 MARK] ii. P(A B) [2 MARKS] iii. P(A|C) [2 MARKS] iv. Are A and B dependent or independent? Explain [1 MARK] V. Are A and C dependent or independent? Explain [1 MARK]