4. Suppose you face the following lottery. You can earn 1 of 3 possible grades in this class: an "A", a "C", or an "F", with the following probabilities: = = 10 10 0 Your current wealth (w) is $400. It you receive an "A", you gain (e.g. I pay you) $500. However, if you get an "F", you lose 'e.g. you pay me) 5300. If you receive a "C", you DO NOT GAIN OR LOSE anything Assume your utility function, defined over wealth, is U (w) = (w).5. i) What is your expected utility (EU)? { lint: be sure to calculate your total wealth in each "state".]