Alex can affect the probability that his car gets in an accident based on the amount of caution c he exercises (by defensive driving, for instance). The probability of an accident occurring is Alex's total wealth is $50 (units in thousands); if an accident occurs, he will lose some fraction of his wealth. y is uniformly distributed from 0 to 1, and does not depend on c.. 1. Continue with Alex's car insurance described in the warmup, with the following change: If an accident occurs, Alex first has to pay a deductible 6, after which his insurance fully reimburses any remaining damage. If the damage is less than the deductible, he simply pays for it out of pocket. (a) Setup Alex's expected utility for a given c and 6, and evaluate the inte- grals. (b) How much caution will he choose to exercise (as a function of 6)? What is the expected damage? (e) What level of deductible will maximize Alex's expected utility (taking into account how his caution varies with the deductible)?