Let U$($x$)=1$e$2$x be a utility function. Consider an investment whose payo isuniformly distributed over $[1,1].($a$)$ Evaluate the investment using the Expected Utility criterion, and find the cer$-$tainty equivalent and the risk premium. What does the sign of the risk premiumtell you about the utility function U$?($b$)$ Using the same utility function, evaluate an investment whose payout is normallydistributed with mean $=0$ and variance $2=1.$ What is the certainty equiva$-$lent?$($c$)$ Which investment would you choose? Give reasons for your answer based on parts$($a$)$ and $($b$)$ above