Question: Here is a dice game. You roll a dice once. If you get 6 you win. If you get 1 you lose.Otherwise you keep rolling

Here is a dice game. You roll a dice once. If you get 6 you win. If you get 1 you lose.Otherwise you keep rolling until you either roll a 2 or a 3 or a 4 or a 5. If you roll a 2 or a 3 or a 4 you win, and if you roll a 5 you lose. Let X denote the number of rolls

(a)FindE(X) using the law of total expectation.

(b )Find a set of difference equations that characterize the PMF of X along with initial conditions.

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