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Bernoulli distribution SAM.

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Binary variables that are random variables are distributed according to a Bernoulli distribution.
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It is the generalization of the Bernoulli distribution for a categorical random variable.
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Every cumulant is just "n" times the corresponding cumulant of the corresponding Bernoulli distribution.
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The first part concludes with what is now known as the Bernoulli distribution.
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The special case 1 is a Bernoulli distribution.
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They all have the same Bernoulli distribution.
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In some contexts, uncorrelatedness implies at least pairwise independence (as when the random variables involved have Bernoulli distributions).
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Such a usage is liable to cause confusion, just as if Bernoulli distributions and binomial distributions were commonly conflated.
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