An instructor has given a short quiz consisting of two parts. For a randomly sel

Question

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(xy) 05 10 15 0.01 0.06 0.02 0.10 x 50.04 0.16 0.20 0.10 100.01 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)? (Give answer accurate to 2 decimal places.) (b) If the maximum of the two scores is recorded, what is the expected recorded score? (Give answer accurate to 2 decimal places.)

Explanation / Answer

X+Y Probability Expected 0 0.01 0 5 0.1 0.5 10 0.19 1.9 15 0.45 6.75 20 0.24 4.8 25 0.01 0.25 14.2 Max Probability Expected 0 0.01 0 5 0.26 1.3 10 0.52 5.2 15 0.21 3.15 9.65

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