Question 1087494
The above isn't clear, but I will give you the distribution for all 11 possibilities
2 is 1/36, product 2/36
3 is 2/36,product is 6/36
4 is 3/36, product is 12/36
5 is 4/36, product is 20/36
6 is 5/36, product is 30/36
7 is 6/36, product is 42/36
8 is 5/36, product is 40/36
9 is 4/36, product is 1
10 is 3/36, product is 30/36
11 is 2/36, product is 22/36
12 is 1/36, product is 12/36
sum of x*p(x) is expected value and is 252/36 or 7, which is the most common roll, and in a symmetrical mass function, the unique middle should be the expected value.
variance is sum of squares of the difference * probability
for 2, 25*1/36 or 25/36
for 3, 16*2/36 or 32/36
for 4, 9*3/36=27/36
for 5, 4*4/36=16/36
for 6, 1*5/36=5/36
for 7,0
for 8, 1*5/36=5/36
for 9,4*4/36=16/36
for 10,9*3/36=27/36
for 11,16*2/36=32/36
for 12, 25*1/36=25/36
sum is 210/36=5.8333
sqrt of that is sd=2.42