continuous uniform distribution

均匀分布

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

Translation evidence: Literature usage

Meaning in context

For real a<ba<b, the law with density 1/(b−a)1/(b-a) on [a,b][a,b] and zero elsewhere.

有限非退化区间上的连续分布，密度在该区间内恒为区间长度的倒数，在外为0。

Example

Uniform probability on [2,6][2,6] assigns probability 1/41/4 to [3,4][3,4].

Usage and distinctions

This record concerns a real interval; a discrete uniform law uses equal masses, and endpoints do not change this continuous law.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on ProbabilitySection 3, Exercise 3.8(i), uniform law on [0,1] and density · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程（北京大学）§1.2.3.9 均匀分布 · Checked 2026-10-14
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