24 lines
740 B
Markdown
24 lines
740 B
Markdown
---
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title: Realization
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tags: []
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---
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# Realization
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> In [[probability]] and [[statistics]],
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> a **realization** or **observation**
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> (also called **observed value**)
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> of a random variable or random element
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> is the value that is actually observed or measured.[^1]
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[^1]: [Realization (probability) - Wikipedia](https://en.wikipedia.org/wiki/Realization_\(probability\))
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> In probability theory,
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> a random variable is a function $X$
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> defined from a sample space $\Omega$ to the state space.
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> If an element in $\Omega$ is mapped to an element in state space by $X$,
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> then that element in state space is a realization.
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> That is, at a point $\omega \in \Omega$,
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> the value $x = X(\omega)$
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> is called a realization of $X$
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