Question: 3. Let X equal the larger outcome when a pair of 6-sided dice are rolled. (a) Assuming the two dice are independent, show that

3. Let X equal the larger outcome when a pair of 6-sided

3. Let X equal the larger outcome when a pair of 6-sided dice are rolled. (a) Assuming the two dice are independent, show that the probability function of X is f(x)= 2r-1 36 x = 1,...,6 (b) Confirm that f(x) is a probability function. (e) Find the mean of X. (d) Can you generalise E(X) to a pair of fair m-sided dice? [Hint: recall that i=n(n+1)/2 and = n(n+1)(2n +1)/6]

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