YES or NO. If your answer is yes, give an explanation in your own words. If your answer is no, provide a counter example. You are welcome to use examples from lecture, if applicable, or make your own. Let X be a random variable with outcome space, S. a) (0.5 pt) Recall the relation between X and S in the definition of a random variable. Is it necessary for S to be the same as the space of X? b) (0.5 pt) Consider a discrete random variable X. Is X's space countable? Is S always countable? c) (0.5 pt) If P(A B) > 0, does the overlap mean that A and B must be dependent