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In probability theory, a probability space or a probability triple is a mathematical construct that models a real-world process (or "experiment") consisting of states that occur randomly. A probability space is constructed with a specific kind of situation or experiment in mind. One proposes that each time a situation of that kind arises, the set of possible outcomes is the same and the probability levels are also the same.
A probability space consists of three parts:
An outcome is the result of a single execution of the model. Since individual outcomes might be of little practical use, more complex events are used to characterize groups of outcomes. The collection of all such events is a σ-algebra Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle \mathcal{F} . Finally, there is a need to specify each event's likelihood of happening. This is done using the probability measure function, P.
Once the probability space is established, it is assumed that “nature” makes its move and selects a single outcome, ω, from the sample space Ω. All the events in Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle \mathcal{F}
This page contains text from Wikipedia, the Free Encyclopedia -
http://en.wikipedia.org/wiki/Probability_space
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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