1. Miles is considering Whether he an an \"A\

1. Miles is considering whether he an an "A", 'B" , or "C" student. His initial belief is that there is a .6 chance that he his an "A" student, a .2 chance that he is a 'B student and a .2 chance that he is a "C" student. He knows that his exam scores are correlated with his true ability- if he is an "A" student he will receive an "a" on the exam with probability .8, a "b" on the exam with probability .1, and a "c" on the exam with probability . 1. If he is a 'B" student he will receive an "a" on the exam with probability . 1. a "b" on the exam with probability .8, and a "c" on the exam with probability . 1. If he is a "C" student, he will receive an "a" with probability .1, a "b" with probability .1, and a "c" with probability .8. (a) If Miles receives an "a" on his exam, what is his updated belief that he is an "A" student? (b) If Miles receives a "b" on his exam, what is his updated belief that he is an "A" student? Now, suppose that Miles has confirmation bias. Whenever he receives a grade that goes against his prior that he is an "A" student, he misremembers it with probability .5. (c) (d) What is Miles' updated belief that he is an "A" student if he remembers an on the exam? (Assume he is sophisticated about his bias.) What is Miles' updated belief that he is an "A" student if he remembers a on the exam? (Assume he is sophisticated about his bias.) Explain why your answer from (b) and (d) differ. [2-4 sentences] a"