Instructions: i) When in doubt, round numeric responses to two decimal places ii) It is okay to discuss the course material with your peers, but please solve all the questions independently and write all your responses in your own words. On the coversheet, please write and sign the following honor pledge: \"I pledge on my honor that 1 have not given or received any unauthorized assistance on this problem set.\" iii) Please submit your assignment by the deadline. Late assignments would not be accepted. Problems: 1) Search and Satisficing: Suppose the utility of items is distributed uniformly randomly over [0,1]. Search cost is k = .125. You have already searched M 1 out of M items, and the best out of those M 1 item give a utility of a. What is the threshold value of @, that makes vou indifferent between searching once more, and not searching? What would be the value of @ if k = .1 instead? Hint: The roots of the quadratic equation az? + bz + = ( jg by dac "21_4'". 2) Base rate neglect: Suppose one of out every 1000 people have COVID on average. The current test has 0% false negative rate, that is 0 out of 100 people who actually have the disease, test negative. The current test has 5% false positive rate, that is 5 out of 100 people who actually don't have the disease, will test positive. What is the chance that a person found to have a positive test result actually has COVID