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Bernoulli

One uncertain yes/no outcome—the atom from which binomial counts are built.
Type discreteSupport {0, 1}Family Counting
Probability massP(X=x) = pˣ(1−p)¹⁻ˣ
discrete

Bernoulli in motion

-0.50.00.51.01.5
Support{0, 1}
Mean0.5
Variance0.25
Connections

Where the bernoulli
comes from — and leads.

Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.

BinomialΣ iid trials

A sum of n independent Bernoulli(p) variables is Binomial(n,p).

TransformationBinomial← n = 1

A binomial with one trial is Bernoulli.

Special caseBeta← p ~ Beta

Beta is conjugate to Bernoulli likelihood; posterior parameters add successes and failures.

Bayesian

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The relationship map draws the whole backbone — special cases, transformations, limits, and conjugacies — in one guided view.

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