Toss a fair coin 10 times. Let N be the number of times the pattern HHHH occurs. For example, in the sequence HHHHHHT, it occurs three times. Find E{N}
2026-03-31 14:33:26.1774967606
Expectation of discrete random variable
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Assuming a fair coin, any sequence of a given length is equally likely. We have $10 - 4 + 1 = 7$ possible sub-sequences of length $4$ and a total of $2^4 = 16$ different H T patterns; resulting in an expected value of $7/16=0.4375$