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LearnProbabilityMechanisms, distributions, transformations, and limits.Bayesian learningPosterior updates, Thompson sampling, and Bayesian optimization.Deep learningActivations, likelihood-derived objectives, and the architectures built from them.01Activations02Likelihood to loss03ObjectivesSemi-supervisedUse a few labels and many unlabeled examples without hiding the assumptions.ReferenceDistributionsRelationship mapSource & method

Poisson

Counts independent arrivals in a fixed exposure; a sparse-event limit of the binomial.
Type discreteSupport {0, 1, …}Family Counting
Probability massP(X=k) = e⁻λ λᵏ / k!
discrete

Poisson in motion

-0.53.37.01115
Support{0, 1, …}
Mean5
Variance5
Connections

Where the poisson
comes from — and leads.

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

Binomial← n→∞, np=λ

Rare independent events converge to a Poisson count.

Limiting resultNormalλ→∞

A centered, scaled Poisson variable approaches standard normal.

Limiting result

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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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