From f11e3c909c5d3e219bebe472411d735dce20e061 Mon Sep 17 00:00:00 2001 From: Zane Meyers Date: Tue, 21 Apr 2026 17:54:23 -0400 Subject: [PATCH] vault backup: 2026-04-21 17:54:23 --- realization.md | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) create mode 100644 realization.md diff --git a/realization.md b/realization.md new file mode 100644 index 0000000..da8ee24 --- /dev/null +++ b/realization.md @@ -0,0 +1,23 @@ +--- +title: Realization +tags: [] +--- +# 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 $X$