Normal Distribution

X ~ N(μ, σ²)

Location-Scale Family • Published July 18, 2026

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About This Reference Sheet

The bell curve: history from de Moivre through Gauss and Laplace, the density and CDF, what location and scale mean geometrically, the full moment/entropy/hazard/quantile property list, maximum-likelihood estimation of the mean and variance, and how to simulate draws via the Box–Muller transform.

Support

x ∈ (-∞, ∞)

Parameters

μ ∈ ℝ (mean), σ² > 0 (variance)