$1.$ Let U$($x$)=1$ e $2$x be a utility function. Consider an investment whose payoff is uniformly distributed over $[1,1].($a$)$ Evaluate the investment using the Expected Utility criterion, and find the certainty equivalent and the risk premium. What does the sign of the risk premium tell you about the utility function U$?($b$)$ Using the same utility function, evaluate an investment whose payout is normally distributed with mean $=0$ and variance $2=1.$ What is the certainty equivalent? $($c$)$ Which investment would you choose? Give reasons for your answer based on parts $($a$)$ and $($b$)$ above. $2.$ Let U$($x$)=$e $$x be a utility function. Consider an investment whose payoff is normally distributed with mean $=2$ and variance $2=0\mathrm{.}5.$ Evaluate the investment using the Expected Utility criterion, and find the certainty equivalent and the risk premium