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Can the sum of identically distributed dependent Bernoulli trials be binomially distributed?

That's false even for $n=3$. Denote by $B(p)$ the Bernoulli distribution which has probability $p$ of being 1 and $(1-p)$ to be 0. Define the three Bernoulli variables $(X_1, X_2, X_3)$ by $ X_1 \si …
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