In a certain board game, one part of the play of the game requires you to keep rolling a pair of dice until you roll "doubles" (both dice showing the same number). Note that with fair six-sided dice the chance of rolling doubles is 1/6, and all rolls are independent of each other. Let X be the number of rolls it takes until you get doubles (including that final roll). Then X has a geometric distribution.

a) (3) Determine the probability that it takes exactly 6 total rolls to first get doubles.

b) (3) Determine the mean and variance of X.

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