(a) Two ordinary dice with faces labelled 1, . . . , 6 are thrown. What is the probability distribution of the sum of the values? What is the probability distribution of the absolute difference between the values?

(b) One hundred ordinary dice are thrown. What, roughly, is the probability distribution of the sum of the values? Sketch the probability distribution and estimate its mean and standard deviation

(c) How can two cubical dice be labelled using the numbers {0, 1, 2, 3, 4, 5, 6} so that when the two dice are thrown the sum has a uniform probability distribution over the integers 1-12?

(d) Is there any way that one hundred dice could be labelled with integers such that the probability distribution of the sum is uniform?