4. (30 points) Determine, in each pair of random variables, if one second order stochastically dominates the other. If so, verify for a strictly increasing and concave utility function (say v(x) = x) prefers the dominating distribution to the dominated one (note that I am only asking you to go through an example, a much easier task than proof of the SSD theorem). If not, give two strictly increasing and concave vNM utility functions, v and w, such that an agent with utility v prefers X to Y, while an agent with utility w prefers Y to X. Deter- mine also whether one is a mean-preserving spread of the other. (a) X and Y are the discrete random variables in Table 1. (b) The example given in class. Namely, X and Y are both random variables on [0, 1]. The pdf of X is given by f(x) = 3/2 - 2x for x = [0, 1/2] and f(x) = 3/2 2(1 x) for x = [1/2, 1]. The pdf of Y is given by g(x) = 24x for x = [0, 1/2] and f(x) = 24(1-x) for x = [1/2,1]. -