18. An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X 

the number of points earned on the rst part and Y

the number of points earned on the second part.

Suppose that the joint pmf of X and Y is given in the accompanying table.

y p(x, y) 0 5 10 15 0 .02 .06 .02 .10 x 5 .04 .15 .20 .10 10 .01 .15 .14 .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?