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| {{About|probabilistic experiments|a more general discussion|Experiment}}
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| {{Probability fundamentals}}
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| In probability theory, an '''experiment''' or '''trial''' (see below) is any procedure that can be infinitely repeated and has a well-defined [[Set (mathematics)|set]] of possible [[Outcome (probability)|outcomes]], known as the [[sample space]].<ref>{{cite web |url=http://www-math.bgsu.edu/~albert/m115/probability/sample_space.html |title=Listing All Possible Outcomes (The Sample Space) |last=Albert |first=Jim |date=21 January 1998 |publisher= Bowling Green State University |accessdate=June 25, 2013}}</ref> 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 events|mutually exclusive]]) possible outcomes is known as a [[Bernoulli trial]].<ref>{{cite encyclopedia | last = Papoulis | first = Athanasios | contribution = Bernoulli Trials | title = Probability, Random Variables, and Stochastic Processes | edition = 2nd | url = http://www.mhhe.com/engcs/electrical/papoulis/ | location = New York | publisher = [[McGraw-Hill]] | pages = 57–63 | year = 1984}}</ref>
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| When an experiment is conducted, one (and only one) outcome results— although this outcome may be included in any number of [[Event (probability theory)|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 probability|empirical probabilities]] of the various outcomes and events that can occur in the experiment and apply the methods of [[Statistics|statistical analysis]].
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| ==Experiments and trials==
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| Random experiments are often conducted repeatedly, so that the collective results may be subjected to [[Statistics|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.<ref>{{cite web | publisher = Future a/ccountant | title = Trial, Experiment, Event, Result/Outcome | url = http://www.futureaccountant.com/probability/study-notes/trial-result-event-outcome.php | accessdate = 22 July 2013}}</ref>
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| ==Mathematical description==
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| {{main|Probability space}}
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| 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.
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| A mathematical description of an experiment consists of three parts:
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| # A [[sample space]], Ω (or ''S''), which is the [[Set (mathematics)|set]] of all possible [[Outcome (probability)|outcomes]].
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| # A set of [[Event (probability theory)|event]]s <math>\scriptstyle \mathcal{F}</math>, where each event is a set containing zero or more outcomes.
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| # The assignment of [[probability|probabilities]] to the events— that is, a function ''P'' mapping from events to probabilities.
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| 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]]'' <math>\scriptstyle \mathcal{F}</math>. Finally, there is a need to specify each event's likelihood of happening; this is done using the ''[[probability measure]]'' function, ''P''.
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| 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 <math>\scriptstyle \mathcal{F}</math> 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 [[Limit (mathematics)|approach]] agreement with the values ''P'' assigns them.
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| ==See also==
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| * [[Probability space]]
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| ==References==
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| {{reflist}}
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| [[Category:Probability theory]]
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Hello!
My name is Shella and I'm a 30 years old boy from Australia.
Feel free to visit my blog post :: craft