nLab moment

This article is on the concept of moment in probability theory. On some pages ‘moment’ is being used for idempotent (∞,1)-monad, e.g., see negative moment.

Definition

For $\mu$ a probability measure on the real line $\mathbb{R}$, its $n$th moment for $n \in \mathbb{N}$ is the expectation value of $x^n$.

Properties

• Moments of Gaussian probability distributions have a combinatorial expression by Wick's lemma.

Related concepts

• expectation value

• Feynman diagram