Sample space
In probability theory, the sample space of an experiment or random trial is the set of all possible 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 "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 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
- Sample space @ Wikipedia.org
