A pair of dice is rolled 3 times and each time the sum Si is

A pair of dice is rolled 3 times, and each time the sum Si is observed. What is the expected value of the product of the Si ?

Solution

Here are all 36 possible rolls with a pair of dice and thier sum: (1,1 = 2) (1,2 = 3) (1,3 = 4) (1,4 = 5) (1,5 = 6) (1,6 = 7) (2,1 = 3) (2,2 = 4) (2,3 = 5) (2,4 = 6) (2,5 = 7) (2,6 = 8) (3,1 = 4) (3,2 = 5) (3,3 = 6) (3,4 = 7) (3,5 = 8) (3,6 = 9) (4,1 = 5) (4,2 = 6) (4,3 = 7) (4,4 = 8) (4,5 = 9) (4,6 = 10) (5,1 = 6) (5,2 = 7) (5,3 = 8) (5,4 = 9) (5,5 = 10) (5,6 = 11) (6,1 = 7) (6,2 = 8) (6,3 = 9) (6,4 = 10) (6,5 = 11) (6,6 = 12)