Question: We keep rolling a fair die until we first roll a 6. Let X denote the sum of the numbers rolled before (and not including)

We keep rolling a fair die until we first roll a 6. Let X denote the sum of the numbers rolled before (and not including) that 6. Calculate: the generating function of X, the expectation of X, the variance of X. (Warning: What is the conditional distribution of a number rolled under the condition that it is not a 6?)

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