Let X be annual income and Y be annual hours worked. Moreover, XN(50000, 150002), YN(2000, 2002), and cov(X, Y)=1, 500, 000. (a) What share of people have annual income greater than than $65,000? (b) What share of people work fewer than 1600 hours a year? (c) Let the joint pdf of X and Y be f(x, y). Write an expression for the share of people who both earn more than $65,000 and work less than 1600 hours in a year? [No need to provide a number, just compose the expression in terms of f(x, y).] (d) Suppose instead that cov(X, Y)=0. Then what would be number associated with your expression above? That is, what is the share of people who both earn more than $65,000 and who work less than 1600 hours.

(Small) Bonus Problem (: Provide a number for part (c). Briefly explain your method or show your work.