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Oct 4, 2022 at 12:26 comment added Timothy Chow Your concluding example can be calculated by hand when $n=3$. The probability of getting $11$ is $1/8$ and the probability of getting $00$ is $1/2$. If the sequence were i.i.d. then we would have to have $\Pr(1) = 1/\sqrt{8}$ and $\Pr(0) = 1/\sqrt{2}$ , but $1/\sqrt{8} + 1/\sqrt{2} \ne 1$.
Oct 3, 2022 at 23:56 vote accept Andras Farago
Oct 3, 2022 at 21:11 history became hot network question
Oct 3, 2022 at 13:35 answer added Iosif Pinelis timeline score: 19
Oct 3, 2022 at 13:07 history asked Andras Farago CC BY-SA 4.0