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Sample space

In a probabilistic experiment, the sample space is the set of all possible outcomes of the experiment.

Notation

Customarily, the sample space is denoted by the Greek letter Omega (Omega). A possible outcome, which can also be called a sample point, is indicated as omega in Omega, where omega (omega) is the lowercase version of Omega.

The letter Omega is the last letter of the Greek alphabet and it is often linked to the idea of something omnicomprehensive (in our case the set of all things that can possibly happen). See also the related Wikipedia article.

Example

Suppose the probabilistic experiment is the toss of a dice. The six numbers that can appear face up, from 1 to 6, are the 6 possible outcomes of the experiment. Hence, the sample space is:[eq1]

More details

A detailed presentation of the concept of sample space - including a discussion of the properties that a sample space needs to satisfy - can be found in the lecture entitled Probability.

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