Here are all 100 possible rolls of two 10-sided dice (computer generated):
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8) (1,9) (1,10)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) (2,8) (2,9) (2,10)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (3,7) (3,8) (3,9) (3,10)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (4,7) (4,8) (4,9) (4,10)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (5,7) (5,8) (5,9) (5,10)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (6,7) (6,8) (6,9) (6,10)
(7,1) (7,2) (7,3) (7,4) (7,5) (7,6) (7,7) (7,8) (7,9) (7,10)
(8,1) (8,2) (8,3) (8,4) (8,5) (8,6) (8,7) (8,8) (8,9) (8,10)
(9,1) (9,2) (9,3) (9,4) (9,5) (9,6) (9,7) (9,8) (9,9) (9,10)
(10,1) (10,2) (10,3) (10,4) (10,5) (10,6) (10,7) (10,8) (10,9) (10,10)
Look down the right to left diagonals for the number of rolls for each sum.
The probabilities p(x) are the number of ways divide by 100:
x p(x) x·p(x)
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There is 1 way to get the sum 2 .01 .02
There are 2 ways to get the sum 3 .02 .06
There are 3 ways to get the sum 4 .03 .12
There are 4 ways to get the sum 5 .04 .20
There are 5 ways to get the sum 6 .05 .30
There are 6 ways to get the sum 7 .06 .42
There are 7 ways to get the sum 8 .07 .56
There are 8 ways to get the sum 9 .08 .72
There are 9 ways to get the sum 10 .09 .90
There are 10 ways to get the sum 11 .10 1.10
There are 9 ways to get the sum 12 .09 1.08
There are 8 ways to get the sum 13 .08 1.04
There are 7 ways to get the sum 14 .07 .98
There are 6 ways to get the sum 15 .06 .90
There are 5 ways to get the sum 16 .05 .80
There are 4 ways to get the sum 17 .04 .68
There are 3 ways to get the sum 18 .03 .54
There are 2 ways to get the sum 19 .02 .38
There is 1 way to get the sum 20 .01 .20
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E(X) = Σ[x·p(x)] = 11.00
Answer: 11
Edwin