Let X be the largest outcome in the throws of two dice. In Example 4.8, we found that the probability function of X is given by

(i) Write down the distribution function of X.
(ii) Calculate the expectation of X in two ways: first, using the probability function in the above formula, and then, using the distribution function found in Part (i), and check that the results agree.
Can you find the probability function and the distribution function of X in the case where we have k dice instead of just two dice?

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2x-1 f(x) = P(X = x) = x = 1,2,3,4,5,6. 36