If is the outcome of your first roll and is the outcome of the second roll, then according to the question
Now use the properties of covariancesto find:
If is the outcome of your first roll and is the outcome of the second roll, then according to the question
Now use the properties of covariancesto find:
Or you can say
Find the expected values from these tables
Code:First X 1 2 3 4 5 6 Second 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 First Y 1 2 3 4 5 6 Second 1 0 1 2 3 4 5 2 -1 0 1 2 3 4 3 -2 -1 0 1 2 3 4 -3 -2 -1 0 1 2 5 -4 -3 -2 -1 0 1 6 -5 -4 -3 -2 -1 0 XY First Second 1 2 3 4 5 6 1 0 3 8 15 24 35 2 -3 0 5 12 21 32 3 -8 -5 0 7 16 27 4 -15 -12 -7 0 9 20 5 -24 -21 -16 -9 0 11 6 -35 -32 -27 -20 -11 0