Consider a sequence of independent tosses of a biased coin at times t = 0, 1, 2, . . .. On each toss, the probability of a ’head’ is p, and the probability of a ’tail’ is 1 − p. A reward of one unit is given each time that a ’tail’ follows immediately after a ’head.’ Let R be the total reward paid in times 1, 2, . . . , n. Find E[R] and var(R).

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