2. (15 points) Determine, in each pair, if one second order stochastically dominates the other. If so, verify for a strictly increasing and concave utility function (say 11(3)) 2 (/5?) 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, 12 and 21), such that an agent with utility 'U prefers X to Y, while an agent with utility 'w prefers Y to X. (a) X and Y are the discrete random variables in Table 1. (b) X has distribution F: F(a:) = x, where a: 6 [0,1]. Y has distribution that is represented by the pdf g(:1:) = 2 4:1: for a: E [0,1/2] and g(x) = 12(a: 1/2)2 for a: E [1/2, 1] (of course, F(a:) = 0(1):) = 0 for a: 1)