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 Xthe number of points earned on the first part and Yhber of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table. px, y)0510 15 0 0.01 0.06 0.02 0.10 x 5 10.04 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 + ? (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.)

Explanation / Answer

a) E(X) = 0*0.19+5*0.48+10*0.33 = 5.7

E(Y) = 0*0.06+5*0.35+10*0.38+15*0.21 = 8.7

E(X+Y) = E(X)+E(Y) = 5.7+8.7 = 14.4

b) Maximum of two score is 8.7

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