Suppose, for the families of your country, Y is annual income (measured in thou- sands of $$) for a family and X is the number of children a family has. If a family's "income per child" (i.e., Y X ) is less than $50,000 then they receive a $2,000-per-child tax credit. [For the purposes of this problem, treat both Y and X as continuous random variables, so that you may think of f ( x, y ) as a joint pdf.] (a) Do you think X and Y are correlated? Explain in two or so sentences. [You can't show this mathematically here! This question is asking you to think about the world. The important part of your response coming up with a reasonable explanation.] (b) Given your response above, do you think f ( x, y ) = f X ( x ) f Y ( y ) ? Explain. (c) Write an expression (using a double integral of course) for the share of families that qualify for the tax credit. [Your response will be in terms of f ( x, y ) . You cannot provide a number here.] (d) Suppose there are N families. What is the expected