Question: Suppose that you toss a fair coin until a head appears and count the number X of consecutive tails that precede it. (a) Determine the

Suppose that you toss a fair coin until a head appears and count the number X of consecutive tails that precede it.

(a) Determine the probability that exactly n consecutive tails occur.

(b) Determine the average number of consecutive tails that occur.

(c) Write down the infinite series that gives the variance for the number of consecutive tails. show that the variance equals 2.

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