World Library  
Flag as Inappropriate
Email this Article

Experiment (probability theory)

Article Id: WHEBN0019621951
Reproduction Date:

Title: Experiment (probability theory)  
Author: World Heritage Encyclopedia
Language: English
Subject: Bernoulli trial, Arithmetic mean, Probability theory
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Experiment (probability theory)

In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space.[1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one. A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial.[2]

When an experiment is conducted, one (and only one) outcome results— although this outcome may be included in any number of events, all of which would be said to have occurred on that trial. After conducting many trials of the same experiment and pooling the results, an experimenter can begin to assess the empirical probabilities of the various outcomes and events that can occur in the experiment and apply the methods of statistical analysis.

Experiments and trials

Random experiments are often conducted repeatedly, so that the collective results may be subjected to statistical analysis. A fixed number of repetitions of the same experiment can be thought of as a composed experiment, in which case the individual repetitions are called trials. For example, if one were to toss the same coin one hundred times and record each result, each toss would be considered a trial within the experiment composed of all hundred tosses.[3]

Mathematical description

A random experiment is described or modeled by a mathematical construct known as a probability space. A probability space is constructed and defined with a specific kind of experiment or trial in mind.

A mathematical description of an experiment consists of three parts:

  1. A sample space, Ω (or S), which is the set of all possible outcomes.
  2. A set of events \scriptstyle \mathcal{F}, where each event is a set containing zero or more outcomes.
  3. The assignment of probabilities to the events— that is, a function P mapping from events to probabilities.

An outcome is the result of a single execution of the model. Since individual outcomes might be of little practical use, more complicated events are used to characterize groups of outcomes. The collection of all such events is a sigma-algebra \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 an experiment is designed and established, it is assumed that “nature” makes its move and selects a single outcome, ω, from the sample space Ω. All the events in \scriptstyle \mathcal{F} that contain the selected outcome ω (recall that each event is a subset of Ω) are said to “have occurred”. The probability function P is defined in such a way that, if the experiment were to be repeated an infinite number of times, the relative frequencies of occurrence of each of the events would approach agreement with the values P assigns them.

See also

References

  1. ^ Albert, Jim (21 January 1998). "Listing All Possible Outcomes (The Sample Space)". Bowling Green State University. Retrieved June 25, 2013. 
  2. ^ Papoulis, Athanasios (1984). "Bernoulli Trials". Probability, Random Variables, and Stochastic Processes (2nd ed.). New York:  
  3. ^ "Trial, Experiment, Event, Result/Outcome". Future a/ccountant. Retrieved 22 July 2013. 
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.