---
tag: 0V5B6D6BQH
kind: concept
name: Characteristic function
aliases: [characteristic-function-of-random-variable]
msc: ["60E10"]
sources:
  - url: https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)
    locator: lead section
same_as:
  wikidata: Q822139
  wikipedia: Characteristic function (probability theory)
---

## Summary

The characteristic function of a real random variable $X$ is the function $t \mapsto E[e^{itX}]$. It is the Fourier transform of the law of $X$, and it exists for every random variable.
The node [[characteristic function|0MYDNRT7PP]] gives the precise definition.