An instructor has given a short quiz consisting of two parts.For a randomly selected student, let X = the number of pointsearned on the first part and Y = the number of points earned on thesecond part. Suppose that the joint pmf of X and Y is given in theaccompanying table.
p(x, y) Â Â Â Â | Â Â 0Â Â | Â Â 5Â Â | Â Â 10Â Â | |
| x | 0 | 0.03 | 0.08 | 0.09 | |
| 5 | 0.09 | 0.20 | 0.20 | |
| 10 | 0.02 | 0.15 | 0.16 | |
(a) what is the probability that a randomly selected studentscores 5 on both parts?
(b) what is the probability that a randomly selected student scoresat least 5 on part 1 and no points on part 2?
(c) find the marginal PMFs of X and Y (find PMF of X and PMF ofY).
(d) If the score recorded in the grade book is the toal numberof points earned in two parts, what is the expected recorded scoreE(X+Y)?
