4-2 Correlation Coefficient: Problem 3 Previous Problem Problem List Next Proble

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4-2 Correlation Coefficient: Problem 3 Previous Problem Problem List Next Problem (1 point) A 4-sided die is rolled twice. Let X be the sum of the two rolls, Y be the first minus the second, and Z be the 5 times the first, minus the second. (a) Compute Cov(X, Y): Cov(X, Y) = 0 (b) Compute Cov(X, Z) Coy(X, Z) 1 Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 50%. You have unlimited attemnts remaining

Explanation / Answer

from above distriution:

for total outcomes are 4*4=16; hence probability of each sample =1/16

from above:

hence Cov(X,Y)=E(XY)-E(X)*E(Y) =0-5*0 =0

Cov(X,Z)=E(XZ)-E(X)E(Z) =55-5*10 =5

x1 x2 X=x1+x2 Y=x1-x2 Z=5x1-x2 P P*X P*Y P*Z P*XY P*XZ 1 1 2 0 4 1/16 1/8 0      1/4 0      1/2 2 1 3 1 9 1/16 3/16 1/16 9/16 3/16 1 11/16 3 1 4 2 14 1/16 1/4 1/8 7/8 1/2 3 1/2 4 1 5 3 19 1/16 5/16 3/16 1 3/16 15/16 5 15/16 1 2 3 -1 3 1/16 3/16 - 1/16 3/16 - 3/16 9/16 2 2 4 0 8 1/16 1/4 0      1/2 0      2      3 2 5 1 13 1/16 5/16 1/16 13/16 5/16 4 1/16 4 2 6 2 18 1/16 3/8 1/8 1 1/8 3/4 6 3/4 1 3 4 -2 2 1/16 1/4 - 1/8 1/8 - 1/2 1/2 2 3 5 -1 7 1/16 5/16 - 1/16 7/16 - 5/16 2 3/16 3 3 6 0 12 1/16 3/8 0      3/4 0      4 1/2 4 3 7 1 17 1/16 7/16 1/16 1 1/16 7/16 7 7/16 1 4 5 -3 1 1/16 5/16 - 3/16 1/16 - 15/16 5/16 2 4 6 -2 6 1/16 3/8 - 1/8 3/8 - 3/4 2 1/4 3 4 7 -1 11 1/16 7/16 - 1/16 11/16 - 7/16 4 13/16 4 4 8 0 16 1/16 1/2 0      1      0      8      total 5      0      10      0      55     

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