Modeling
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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

Standard normal

The parameter-free normal reached by standardizing X to (X−μ)/σ.
Type continuousSupport ℝFamily Location–scale
Probability densityf(z) = exp(−z²/2) / √2π
continuous

Standard normal in motion

-4.0-2.00.02.04.0
Supportℝ
Mean0
Variance1
Connections

Where the standard normal
comes from — and leads.

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

Normal← (X−μ)/σ

Center and scale any normal to obtain Z ~ N(0,1).

TransformationChi-squareΣ Zᵢ²

A sum of k squared standard normals is Chi-square(k).

Transformation

Zoom out

See every connection at once.

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

Open the map