---
title: Realization
tags:
  - topic/math/statistics
---
# Realization

> In [[probability]] and [[statistics]],
> a **realization** or **observation**
> (also called **observed value**)
> of a random variable or random element
> is the value that is actually observed or measured.[^1]

[^1]: [Realization (probability) - Wikipedia](https://en.wikipedia.org/wiki/Realization_\(probability\))

> In probability theory,
> a random variable is a function $X$
> defined from a sample space $\Omega$ to the state space.

> If an element in $\Omega$ is mapped to an element in state space by $X$,
> then that element in state space is a realization.
> That is, at a point $\omega \in \Omega$,
> the value $x = X(\omega)$
> is called a realization of $X$