Expected number of "BOOK"

probability expected-value

Expectation is additive even if the random variables involved are not independent. If some fixed substring $s$ occurs with probability $p(s)$ in first place and probability $p(s)$ in second place, then the expected number of times that this string occurs in first or second place is $2p(s)$, even though the probability that the string appears in both places at once depends on the string in question.


$$\mathbb{E}[X+Y]=\mathbb{E}[X] + \mathbb{E}[Y]$$

That is the expectation of sum is the sum of expectation. The linearity of expection does not require independence.

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