 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/discrete-mathematics-probability-and-continuous-mathematics/8/c/iii/solution

The identity

X Y = (S_{1} + S_{2}) (S_{1} - S_{2}) = S_{1}^{2} - S_{2}^{2}

gives

E [X Y] = 0

, since the two rolls have the same probability distribution. Also

E [X] E [Y] = 7 \cdot 0 = 0

. Therefore

cov (X, Y) = E [X Y] - E [X] E [Y] = 0.

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