4. Consider the probability space (S, M, P) where S = {a, b, c, d ), the set of events M is the power set of S, and P is defined by letting the density function f: S - [0, 1] 1 satisfy f (s) = -. Define the events A = {a, b}, B = {b, c}, and C = {b,d). 4 Which of the pairs of events (A, B), (A, C), and (B, C ) is a pair of independent events? Which of the pairs of events (A n B, C), (A n C, B), and (B n C, A) is a pair of independent events? 5. Consider a continuous random variable X with the probability density function defined by f(x) = c- for x E [5, co) and f(x) = 0 otherwise. 72 What is the value of c? What is the value of E[X ]