Help answering this? The lines indicate a fill in the blank and unless given word options in the parentheses, the answers are integers or variables.

8. (11%) A professional football athlete is uncertain about whether he will suer a severe brain concussion in the sport, but he believes that the probability for him to suffer such a brain concussion is 1/3. If such a brain concussion occurs to him, his income shrinks to 1 million dollars; else his income is 9 million dollars. a. Staying with the above-described profession, the athlete is effectively playing the gamble (lottery) ,ilililili 1) +7 ,,,,,,, i 3; namely, receiving a payoff equal to 1 mil- lion dollars with probability ,,,,,,,,,,,,,,,, , and a payoff equal to 9 million dollars with probability ___.______-_____l The expected value of this gamble is equal to ____.______.____ million dollars. b. Suppose that the athlete's preferences are quantied by the expected utiities based on a vNM utility function u dened by 11(2) := J; for any nonnegative income I measured in million dollars (e.g., the utility of having for sure 2 million dollars is equal to ) i. The athlete's expected utility from the above-described gamble is equa to _________________ ii. Suppose that the athlete is offered an insurance policy that would cost him 1 mil- lion dollars to purchase and, if he purchases it, would pay him 3 million dollars i he suffers a severe brain concussion. This insurance policy corresponds to the __ (3 7 1 + ________________ (71 , and its expected value is equal million dollars. If the athlete buys this insurance policy, with the gamble to ,,,,, insurance policy combined with his profession, he is effectively playing the gamble ,,,,,,,,,,,,,,,, (1 + 3 1 +WWWWWWWW (9 W , which gives him the expected util- ity equal to ___________.____________________, which is _____________ (larger than, less than, equal to, incomparable to) the expected utility of his profession without the insur- ance policy. Thus, the athlete would lllllllllll (buy, not buy, indifferent about buying) the insurance