Problem 5: Consider two random variables Y and X with E[Y] = my, E[X] = Ax, Var(Y) = ory, Var(X) = oxx and Coo(Y, X) = orx. Suppose that you have a set of paired observations (Yi. Xi), (Yo. X,). ....(Y., X) that are drawn i.id. from the joint distribution of the random variable (Y, X). Your goal is to construct confidence intervals of the form [L, for the unknown difference ay - ux. Now answer the following questions. (a) Suppose that Var(Y) = oyy, Var(X) = oxx and Cov(Y, X) = oyx are known. Construct a confidence interval [L, such that it has asymptotic coverage probability of 95%. (b) Suppose that Var(Y) = ory, Var(X) = oxx and Cou(Y, X) = oyx are unknown. Construct a confidence interval [L, such that it has asymptotic coverage probability of 95%