Suppose that a person's score X on a mathematics aptitude test is a number in the interval (0, 1) and that his score Y on a music aptitude test is also a number in the interval (0, 1). Suppose also that in the population of all college students in the United States, the scores X and Y are distributed in accordance with the following joint p.d.f.:

a. If a college student is selected at random, what predicted value of his score on the music test has the smallest M.S.E.?
b. What predicted value of his score on the mathematics test has the smallest M.A.E.?

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