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 first 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.
|
p(x, y)
|
0 |
5 |
10 |
15 |
| x |
0 |
0.01 |
0.06 |
0.02 |
0.10 |
| 5 |
0.04 |
0.14 |
0.20 |
0.10 |
| 10 |
0.01 |
0.15 |
0.16 |
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)? (Enter your answer to one decimal place.)
(b) If the maximum of the two scores is recorded, what is the expected recorded score? (Enter your answer to two decimal places.)