Problem 3. Suppose U and V are two independent, identically distributed uniform [0, 1] random variables. (a) Calculate the joint density of X = max {U, V} and Y = min U, V. (b) Compute the covariance of X and Y. (c) Find E[Y X] and E[X|Y]. (d) Determine the linear predictor of Y in terms of X, Y = aX + b, that has minimal mean squared error, i.e. so that E[Y - Y]2 is minimized