Question 8 Consider the probability space defined by (S, M, P) where S = {a, b, c, d, e, f], the set of events M is the power set of S, and P is defined by the density f (s) = = for all s E S. Let X be the random variable on this probability space defined by X (a) = X(b) = X(c) = 1 and X(d) = X(e) = X(f) = 0. Define Y by Y(a) = Y(d) = 2, Y(b) = Y(c) = Y(e) = Y(f) = 3. Are these random variables independent