Karl Jones: Created page with "In probability theory, the '''sample space''' of an experiment or random trial is the set of..."

2016-09-14T03:26:43Z

Created page with "In probability theory, the '''sample space''' of an experiment or random trial is the set of..."

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In [[probability theory]], the '''sample space''' of an [[Experiment (probability theory)|experiment]] or random [[Trial and error|trial]] is the [[Set (mathematics)|set]] of all possible [[Outcome (probability)|outcomes]] or results of that experiment.

== Description ==

A sample space is usually denoted using [[set notation]], and the possible outcomes are listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for "[[Universe (mathematics)|universal set]]").

For example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}. For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}. For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).

A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined [[Set (mathematics)|set]] of possible events (a [[sigma-algebra]]) and a probability assigned to each event (a [[probability measure]] function).

== See also ==

* [[σ-algebra]]
* [[Event (probability theory)]]
* [[Probability space]]
* [[Space (mathematics)]]
* [[Set (mathematics)]]
* [[Universe (mathematics)]]

== External links ==

* [https://en.wikipedia.org/wiki/Sample_space Sample space] @ Wikipedia.org

[[Category:Mathematics]]

Sample space - Revision history

Karl Jones: Created page with "In probability theory, the '''sample space''' of an experiment or random trial is the set of..."