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

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.

y

p(x, y)

     
  0      5      10      15   
x 0 0.03 0.06 0.02 0.10
5 0.04 0.15 0.20 0.10
10 0.01 0.15 0.13 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.)

_________________

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