A lecturer has given a test consisting of two parts. For a randomly selected student, let X be the number of points earned on the first part and Y be the number of points earned on the second part. Suppose the joint pdf of X and Y is given in the following table: X Y 0 5 10 15 0 0.02 0.06 0.02 0.10 5 0.04 0.15 0.20 0.10 10 0.01 0.15 0.14 0.01 (a) If the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score E(X+Y)? (b) If the maximum of the two scores is recorded, what is the expected recorded score? (c) Compute the covariance for X and Y (d) Compute the correlation for X and Y