Question 1: Answer the following questions: 1. There are three alternatives X E {3:1, 1:2, 1:3}. Explain whether or not the following two VNM utility functions, a and '31, represent the same preference over lotteries. 16(131) = 3, \"4:32) 2 6, 11,053) = 7. Eln) = 100, 53(182) = 200, ($3) = 250. 2. Suppose Adam's preference admits a subjective expected utility representation and his VNM utility function over money is 1:.(10) = 11:. He faces uncertainty in terms of whether it will be rainy or sunny tomorrow. He is indifferent between the following two acts: (a) Winning 2 dollars if it is rainy, and losing 5 dollars if it is sunny; (b) Losing 4 dollars if it is rainy, and winning 2 dollars if it is sunny, What is Adam's subjective belief about tomorrow's weather (that is, chances that it will be rainy, and chances that it will be sunny)