Question: Alex is given the choice between two games. In Game 1, a fair coin is flipped and if it comes up heads, Alex receives

Alex is given the choice between two games. In Game 1, a

Alex is given the choice between two games. In Game 1, a fair coin is flipped and if it comes up heads, Alex receives $100. If the coin comes up tails, Alex receives nothing. In Game 2, a fair coin is flipped twice. Each time the coin comes up heads, Alex receives $50, and Alex receives nothing for each coin flip that comes up tails. Assuming that Alex has a monotonically increasing utility function for money in the range \[$0, $100\], show mathematically that if Alex prefers Game 2 to Game 1, then Alex is risk averse (at least with respect to this range of monetary amounts). Show that if X1 and X2 are preferentially independent of X3, and X2 and X3 are preferentially independent of X1, then X3 and X1 are preferentially independent of X2.

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