Fred Has an Income of $1,000 $$U = \sqrt { X }$$

Essay

Fred has an income of $1,000. He can participate in a lottery in which he has 50 percent probability of getting an additional $500. Otherwise, he loses $500. Compute expected Fred's income if he participates in the lottery. What is his expected utility of the income if his utility function is $$U = \sqrt { X }$$ . Should he buy the ticket?