25 lines
763 B
Markdown
25 lines
763 B
Markdown
---
|
||
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 $X$
|