All three lotteries have the same expected value of 6. Under the expected value rule, the three lotteries are thus equally attractive. However, the lotteries differ in their riskiness. Consider a risk-averse individual with riskless assets of 5 and the following utility function of final wealth: u(w) = w–0.03·w2. Find the expected utility of each lottery for this individual and rank the lotteries from best to worst. 

+ Lottery X Prob. Payoff 0.5 2 0.5 10 Lottery Y Payoff 2 6 14 Prob. 0.5 0.25 0.25 Lottery Z Prob. Payoff 0.5 0 0.25 10 0.25 14