normal distribution

正态分布

Probability · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: Gaussian distribution · 高斯分布

Translation evidence: Literature usage

Meaning in context

For μ∈R\mu\in\mathbb R and σ>0\sigma>0, the law with density (σ2π)−1exp⁡(−(x−μ)2/(2σ2))(\sigma\sqrt{2\pi})^{-1}\exp(-(x-\mu)^2/(2\sigma^2)) on R\mathbb R.

均值为μ、方差为正数σ²的实数分布，其密度具有对应的高斯指数形式。

Example

The standard normal law is N(0,1)N(0,1).

Usage and distinctions

Here the second parameter of N is variance, not standard deviation; the singular sigma=0 extension must be stated separately.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on Probability§8.2.1 Normal distribution · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程（北京大学）§1.2.3.10 正态分布 · Checked 2026-10-14
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