document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #806915 by Boreal(15235) $\"\"$ $\"About$

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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
\n" ); document.write( "Add 105 from the the part below diagonal and you get 210.
\n" ); document.write( "Divide by 36 and you get 5.833 for the variance and the sqrt of that for the sd
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\n" ); document.write( "Now expand that to 9 x 9.
\n" ); document.write( "The mean will be 10 and that is along the long diagonal. There are 9 possibilities for a probability overall of 1/9.
\n" ); document.write( "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
\n" ); document.write( "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. \n" ); document.write( "

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