2.1 What is the slope of the BLP for Y given X? (Hint: you can calculate this with only the provided f (x, y) with a very simple calculation) 2.2 Prove that cov [X, E] has the form a + bB1 for some constants a, b E R. What is the value of a ? 2.3 Prove that cov [X, E] has the form a + bB1 for some constants a, b E R. What is the value of b ? 2.4 How is the sign of cov [X, c] is related to the angle of the line g? (select all that are true) if cov[ X, E] is positive, the slope of g is greater than the slope of the BLP. if cov[ X, E] is positive, the slope of g is less than the slope of the BLP. if cov[X, E] is negative, the slope of g is greater than the slope of the BLP. if cov[ X, E] is negative, the slope of $9$ is less than the slope of the BLP.Suppose that discrete random variables X and Y have joint probability mass function given by: f (2, y) = 0, 1/2, (x, y) E {(0, 0), (2, 1)} otherwise (This means that there is equal probability that the points (0, 0) and (2, 1) are drawn; there is zero probability that any other point is drawn.) Let g(x) = Bo + Biz be a linear predictor for Y that is a function of x, and define the error, E, to be the difference between the true value of Y and the prediction g (X), E = Y - g(X). Assume that the moment condition E E = 0 holds. In the lecture, we proved that this means that g passes through the point (E[X], E[Y] ) (In some places, this point is referred to as the grand mean.) We want to compute the covariance between X and E. Because how how we have defined E, we know that the computation probably starts with a substitution