There are two octahedral dice with faces marked 1 through 8. They are constructed such that the side 8 is 1.5 times as probable as the 2 through 7 and the sum of the probabilities of the 1 and the 8 equals that of the pairs on opposing faces. Let x be the sum of the faces when we roll the two dice. Find the following: a. Probability distribution of x b. Mean of x c. Variance of x