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

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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)?

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3.9 Ratings (393 Votes)

Note that total probability is always equal to 1 So please check the given probabilities Here total of the probabilities 102 Lets take PX 10 Y 10 014 instead See Answer

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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