1. (15 points) Now consider the following pairs of random variables, X and Y. Determine, in each pair, if one first order stochastically dom- inates the other. If so, demonstrate that an agent with a strictly increasing utility function always prefers the dominating distribution to the dominated one, i.e., reproduce the rst half of the FSD Theorem for the particular distributions given. If not, give an example of two strictly increasing vNM utility function, e and to, such that an agent with utility n prefers X to Y, While an agent with utility in prefers Y to X. Table 1: distributions of X and Y (a) X and Y are discrete random variables. Their probabilities of taking each possible value is listed in Table 1. (b) X has distribution F, F(m) = 1 e'3 and Y has distribution G, C(33) = l 2'3, where I 2 G (of course, F(:r) = C(m) = U for a: s: U)