1. (20 points) Answer the following concept questions. (a) If two events are mutually exclusive, are they independent as well? (b) If three events form a partition of a sample space, what is true about the probabilities of those three events? (c) In general, is the conditional probability of two events smaller or larger than the joint probability ? (d) I have calculated that the CDF of a random variable X is 0.1 when x = 1 and 0.09 when x = 2. Do you have enough infor- mation to know if I have done this correctly, and if so, did I get it right ? (e) I have two coins. One is fair and one isn’t. Which one will have the higher entropy ?