Please solve this problem.

2. Best Linear Predictor of a Constrained Outcome Space Suppose that discrete random variables X and Y have joint probability mass function given by: ay) = {1/21 (may) E{(D,UL(2,1)} 0, otherwise (This means that there is equal probability that the points ((1, U} and (2, 1) are drawn; there is zero probability that any other point is drawn.) Let 9(a) : 1% + ,Bla: be a predictor for y that is a function of 2:, and dene the error, E, to be the difference between the true value of y and the prediction 9(a), e = Y 9(X]. 1. (1 point} If you impose the moment condition (that is, you require that), E[E] = 0, what one point in the plane must the predictor pass through? (In some places, this point is referred to as the grand mean.) 2. (2 points) Because we have dened E = Y 9(X), we can ask the question, \" What is the covariance between X and E 1?\" Because how how we have dened E, we can know that the answer probably starts with a substitution: Cov[X,] = Coe[X,Y 9(3)] Assmne {or you might say, \"require\") that the expected value c is zero, E[E] : D. Then, prove that coulX, E] has the form a+ 5,61. Given the constraints of the pd f(23, 3;), you have been provided, what is the specic value of b? 3. [2 points) How is the sign of coung] is related to the angle of the line. 4. [2 points] Compute the BLP in this way: a. Assume (or you might say require} that E[] : D. h. Then, set COUIX,] = [l and solve for ,81. What is the value of J31