Question 1177774: Construct the probability distribution for the sum shown on the faces when two dice, each with 9 faces, are rolled. The the mean, variance, and standard deviation
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Write out the matrix for a 6 sided die and there are 36 outcomes, with 7 the most common sum, being along the diagonal, and there are 6 of them. That is your mean. Look above the diagonal. The variance here 1^2*5+2^2*4+3^2*3+4^2*2+5^2*1=105
Add 105 from the the part below diagonal and you get 210.
Divide by 36 and you get 5.833 for the variance and the sqrt of that for the sd
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Now expand that to 9 x 9.
The mean will be 10 and that is along the long diagonal. There are 9 possibilities for a probability overall of 1/9.
Above the diagonal will have 1^2*8+2^2*7+3^2*6+4^2*5+5^2*4+6^2*3+7^2*2+8^2*1=540
Add what is below the diagonal and the sum is 1080. Divide by n, which is 9^2=81, and the variance is 13.33 and the sd is 3.65.
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