3. (20 points) We roll two fair and independent dice, d1 and d2. Let X = max(d1, d2), the maximum of these two dice. (a) (10 points) Let F be the cumulative distribution function of X. Write of F com- pletely, as a piece-wise function, so that F(:t:) is accounted for every :3 E R. (b) (10 points) Let Y = min(d1,d2). Are E, = {X = a} and E, = {Y = b} pairwise independent events? Either (i) nd an example, a. selection of a and b where these events are not independent, or (ii) show that no matter what a and b you may choose the events are independent