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 second part. Suppose that the joint pmf of X and Y is given in the accompanying table the number of points earned on the 0.02 0.04 0.01 0.06 0.17 0.15 10 0.02 0.20 0.12 15 0.10 0.10 0.01 10 (a) Compute the covariance for X and Y. (Round your answer to two decimal places.) Cov(X, )- (b) Compute for X and Y. (Round your answer to two decimal places.)

Explanation / Answer

from above:

marginal pmf of X:

marginal pmf of y:

alos E(XY) =42.75

therefore a) Cov(X,Y) =E(XY)-E(X)E(Y) =-3.30

b)correlation coefficient =Cov(X,Y)/(Var(X)*Var(Y))1/2 = -0.22

y x 0 5 10 15 Total 0 0.0200 0.0600 0.0200 0.1000 0.2000 5 0.0400 0.1700 0.2000 0.1000 0.5100 10 0.0100 0.1500 0.1200 0.0100 0.2900 Total 0.0700 0.3800 0.3400 0.2100 1.0000

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