(20 points) Rolling a fair n-sided die gives us a random number uniformly distributed among {1, 2,...,n} (our usual die is n = 6). Suppose we independently roll a fair n-sided die twice and obtain numbers X1 and X2. (a) Calculate E(max(X1, X2)) and E(min(X1, X2)). (b) Show that your calculation in part (a) verifies that E(max(X1, X2)) + E(min(X1, X2)) = E(X1) + E(X2). (c) Is the above equation simply a coincidence? Can you give a simple and direct proof of it?