Probability theory (6229 bytes)
1: ...'' is the [[Mathematics|mathematical]] study of [[probability]].
3: ...igned to events <math>E</math> according to the [[probability axioms]].
5: ...ath>F</math> is the same as the ("unconditional") probability of <math>E</math>, then <math>E</math> and <math>...
8: ...y are those of a [[random variable]] and of the [[probability distribution]] of a random variable; see those ar...
10: ==A somewhat more abstract view of probability==

Event (probability theory) (2543 bytes)
2: ...e sample space are events), but when defining a [[probability space]] it is possible to exclude certain subsets...
6: ...the sample space itself (which is defined to have probability one). Other events are sets are [[proper subset]...
11: ...robability]], and the definition of [[conditional probability]] can be represented in this fashion.)
13: ... is an event.<br>By the ratio of their areas, the probability of ''A'' is approximately 0.4.</small></center>
15: ==Events in probability spaces==

Probability (21088 bytes)
1: The word '''''probability''''' derives from the [[Latin]] ''probare'' (to p...
5: As with the [[classical mechanics|theory of mechanics]] which assigns precise definitions ...
6: so the [[probability theory|theory of probability]] attempts to quantify the notion of ''probable''...
11: ... has been an interest in quantifying the ideas of probability for millennia, but exact mathematical description...
15: ...ed to fall; continuous errors are discussed and a probability curve is given.

Free probability (1637 bytes)
1: ...and it is connected with [[free product]]s. This theory was introduced by [[Dan Voiculescu (mathematician...
5: ...[[cumulant]] functional plays a major role in the theory. It is related to the lattice of [[noncrossing p...
12: ...tics] - containing a readable description of free probability
17: [[Category:Probability theory]]

Probability of error (1260 bytes)
1: ==Probability of error in hypothesis testing==
7: The '''probability of error''' is similarly distinguished.
11: ==Probability of error in statistical modelling and econometric...
15: ...n to be a [[random variable]] and as such has a [[probability distribution]].

Algorithmic probability (1492 bytes)
1: ...lomonoff]] invented the concept of '''algorithmic probability'''.
6: The algorithmic probability of any given finite output
9: programs have high probability.
11: Algorithmic probability is the main ingredient
12: of [[Ray Solomonoff]]'s theory of [[inductive inference]],

Probability amplitude (2265 bytes)
1: ...nknown quantity. For example, each particle has a probability amplitude describing its position.
3: ...r a probability amplitude &psi;, the associated [[probability density function]] is
7: ...i;|². This is sometimes called just '''probability density''', and may be found used without normali...
9: ...i; by ''c''&psi; the integral becomes 1. Then the probability that a particle is within a particular region ''V...
11: ... expressed in terms of &psi; itself, not just the probability function |&psi;|². See [[Schr&ouml;din...

Coupling (probability) (3102 bytes)
5: ...math>X_1</math> and <math>X_2</math> is a ''new'' probability space <math>(\Omega,F,P)</math> over which there ...
13: ...never meet, we continue this process forever (the probability for that is zero, though). After this event, we c...

Probability and statistics (357 bytes)
1: ...is]] depends on the characteristics of particular probability distributions, and the two topics are normally st...
5: *[[List of probability topics]]
10: [[Category:Probability and statistics|*]]

Exotic probability (1361 bytes)
1: ...g to Youssef, the valid possible alternatives for probability values are the [[real number]]s, the [[complex nu...
3: ...]] and [[S. K. Srinivasan]] as relevant to exotic probability theories.
10: ...bs/hep-th/0110253 Physics with exotic probability theory] - paper by Youssef on [[arXiv]].
13: ...pages.com/home/kmath309.htm The Complex Domain of Probability]
17: [[Category:Probability theory]]

Prior probability (5478 bytes)
1: ...bility''' is a [[conditional probability|marginal probability]], interpreted as a description of what is known ...
2: ...sterior probability]]'' is then the [[conditional probability]] of the variable taking the evidence into accoun...
3: The posterior probability is computed from the prior and the [[likelihood f...
5: ...d ''posterior'' are not terms used in [[frequency probability|frequentist]] analyses,
6: this article uses the vocabulary of [[Bayesian probability]] and [[Bayesian inference]].

Probability of kill (2020 bytes)
3: The Probability of Kill (or PK) is usually based on a Uniform [[r...

Probability space (730 bytes)
4: In [[mathematics]], a '''probability space''' is a [[set]] ''S'', together with a [[si...
5: ...ents of ''X'' are called the [[Event (probability theory)|events]].
6: ...'probability measure'', and ''P''(''E'') is the [[probability]] of the event ''E''.
8: The above is a compact form of stating the [[probability axioms]].
10: Note that not all subsets of a probability space are events.

Appeal to probability (1039 bytes)
1: The '''appeal to probability''' is a [[logical fallacy]], often used in conjun...
9: ... that it is rarely used by itself), the appeal to probability is a common trend in many arguments, enough for m...

Inverse probability (736 bytes)
1: ...erse probability''' is an obsolete term for the [[probability distribution]] of an unobserved variable.
3: ...p''(''x''|&theta;) itself is called the '''direct probability'''.
5: ...stribution" became prevalent. See also [[Bayesian probability]] and [[Bayes' theorem]].
7: [[Category:Probability theory]]

Statistical probability (475 bytes)
1: ...for [[frequency probability]], which identifies [[probability]] with relative frequency over a long series of e...
3: ...bility]], which have in common the application of probability to problems which don't necessarily involve repet...

Probability vector (492 bytes)
1: In [[mathematics]] and [[statistics]], a '''probability vector''' or '''stochastic vector''' is a [[vecto...
3: Here are some examples of probability vectors:

Frequency probability (2045 bytes)
3: ...quency]] [[Probability interpretations|concept of probability]].
9: ...ions|debate]] between frequentists and [[Bayesian probability|Bayesian]]s. The former insisted that statistical...
11: ...f you perform the experiment enough times, is the probability.
17: ...[[statistics]] -- [[statistical regularity]] -- [[probability axioms]] -- [[games of chance]]
21: ...tp://curry.edschool.virginia.edu/teacherlink/math/probability/history/contributors/vonMises.html

Born probability (559 bytes)
1: ...r more generally from the [[density matrix]]. The probability (or its [[density]]) equals the squared modulus o...

Applied probability (1483 bytes)
1: ... probability''', the application of [[probability theory]] to other scientific domains. However, while su...
3: ... the application of [[stochastic process]]es, and probability more generally, to the natural, applied and socia...
21: **[[Queueing theory]].
22: **[[Renewal theory]].
26: ...p://www.shef.ac.uk/uni/companies/apt/ The Applied Probability Trust].

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