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Suppose we toss a fair coin n = 1 million times and write down the outcomes:...

Suppose we toss a fair coin n = 1 million times and write down the outcomes: it gives a Heads-and-Tails-sequence of length n. Then we call an integer i unique, if the i, i + 1, i + 2, i + 3, . . . , i + 18th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the ith element of the sequence. Let Y denote the number of unique integers i. What is the expected value of Y?

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