Normal
The central limit attractor and the default local model for additive noise.
Probability density
f(x) = exp(−(x−μ)²/2σ²) / (σ√2π)continuous
Normal in motion
Supportℝ
Mean0
Variance1
ConnectionsWhere the normal
Where the normal
comes from — and leads.
Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.
Binomial
← np, n(1−p) largeStandardized binomial counts approach the normal law.
Limiting resultPoisson← λ→∞A centered, scaled Poisson variable approaches standard normal.
Limiting resultStandard normal(X−μ)/σCenter and scale any normal to obtain Z ~ N(0,1).
TransformationCauchyZ₁/Z₂The ratio of two independent standard normals is standard Cauchy.
TransformationStudent t← ν→∞As scale estimation uncertainty vanishes, t approaches normal.
Limiting resultZoom out
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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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