You roll two dice at a time. Die 1 has 6 different possible states and die 2 also has 6, making a total of 6 × 6 = 36 different ways the two can land. Suppose that f is the sum of the number of dots showing on the two dice. Calculate the mean value of f per roll using two approaches.
(a) Sum over all 36 configurations the probability of occurrence of a configuration (1/36) times the sum of the dots showing in that configuration.
(b) Noting that the outcomes for the two dice are statistically independent (the probabilities for the second die are independent of the results for the first roll), use the result that
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The two answers should be the same.