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Let there be $n$ Bernoulli trials in some experiment. Define $Y$ as the maximum number of consecutive successes in our experiment. So if $n=10$ and each trial $X_i$ is distributed iid with $X_i \sim \text{Bernoulli}(0.5)$, then our sample could be $(1, 1, 0, 0, 0, 1, 1, 1, 0, 1)$ and $Y=3$.

What is $E[Y]$?

StubbornAtom
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Alex L
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  • This may be of help: https://math.stackexchange.com/questions/59738/probability-for-the-length-of-the-longest-run-in-n-bernoulli-trials – rubikscube09 Oct 07 '20 at 15:52

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