Law of total probability (1125 bytes)
1: Nomenclature in [[probability theory]] is not wholly standard.
3: ... infinite [[partition of a set|partition]] of a [[probability space]] and each set ''B''_''n'' is [[m...
7: This is also sometimes called the ''law of alternatives''.
9: The phrase '''''law of total probability''''' is also used to refer to the proposition tha...
17: ...'N'' is a [[random variable]] equal to ''n'' with probability ''P''(''B''_''n''). It may be stated e...

Law of total variance (2492 bytes)
1: ... same [[probability space]], and the [[variance]] of ''X'' is finite, then
5: ...ance'''; the second is the '''explained component of the variance'''.
7: ...'[[law of total probability]]''. Some writers on probability call this the "conditional variance formula" or b...
9: ...e conventional rigidly case-sensitive notation of probability theory becomes important!). If we write E( ''X''...
11: ==The square of the correlation==

Law of total tricks (3089 bytes)
1: ...bid in a competitive auction. It is not really a law (because counterexamples are easy to find) but it...
3: ... available on a deal is equal to the total number of trump cards both sides hold in their respective b...
5: ... if North-South can take 9 tricks in hearts, the "law" says East-West can take only 7 tricks in spades.
7: The "law" is said to be most accurate when the [[high card...
9: ...g table, it turns out that the following is quite often winning strategy:

Law of total expectation (1210 bytes)
1: ...riable, not necessarily integrable, on the same [[probability space]], then
5: ...X'' given ''Y'' is the same as the expected value of ''X''.
7: ...[[law of total probability]]''. See also [[law of total variance]].
9: ...e conventional rigidly case-sensitive notation of probability theory becomes important!). If we write E( ''X''...
12: [[Category:Probability theory]]

Probability (21088 bytes)
1: The word '''''probability''''' derives from the [[Latin]] ''probare'' (to p...
2: Informally, ''probable'' is one of several words applied to uncertain events or know...
5: As with the [[classical mechanics|theory of mechanics]] which assigns precise definitions to ...
6: ... of probability]] attempts to quantify the notion of ''probable''.
11: ...or millennia, but exact mathematical descriptions of use in those problems only arose much later.

Free probability (1637 bytes)
1: ... property is the analogue of the classical notion of [[statistical independence|independence]], and it...
3: ...are then said to be '''free''' if the expectation of the product ''a''₁...''a''<sub>''n''</...
5: ...tice of ''all'' [[partition of a set|partitions]] of that set.
12: ...tics] - containing a readable description of free probability
17: [[Category:Probability theory]]

Coupling (probability) (3102 bytes)
1: ...cs]], '''coupling''' is a [[Mathematical proof|proof]] technique that allows to compare two unrelated ...
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 space (730 bytes)
4: In [[mathematics]], a '''probability space''' is a [[set]] ''S'', together with a [[si...
5: ...and the elements of ''X'' are called the [[Event (probability theory)|events]].
6: ...easure'', 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.

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:

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: ... be found used without normalisation (to have the total 1).
9: ...articular region ''V'' is the integral over ''V'' of |&psi;|².
11: ... expressed in terms of &psi; itself, not just the probability function |&psi;|². See [[Schr&ouml;din...

Probability of kill (2020 bytes)
1: ... with large numbers of customers and huge numbers of variables.
3: ...a simulation, the average result will be that 30% of the weapon/target engagements will be a kill and ...
5: ... [[surface-to-air missile]] system has a '''PK''' of 0.9 against highly maneuvering targets.
9: A.M. Law and W.D. Kelton, ''Simulation Modeling and Analys...
11: J. Banks (editor), ''Handbook of Simulation: Principles, Methodology, Advances, Ap...

Conditional probability (2168 bytes)
1: ... which characterize [[probability distribution]]s of two or more variables.
3: ...l probability''' is the [[probability]] of some [[Probability/Event|event]] ''A'', assuming event ''B''.
4: ... ''P''(''A''|''B''), and is read "the probability of ''A'', given ''B''".
6: ...ts in conjunction. That is, it is the probability of both events together.
7: The joint probability of ''A'' and ''B'' is written ''P''(''A'', ''B'').

Prior probability (5478 bytes)
1: ... of what is known about a variable in the absence of some [[evidence]].
2: ...ility]]'' is then the [[conditional probability]] of the variable taking the evidence into account.
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]].

Bayesian probability (9139 bytes)
1: ... degree of belief of rational agents in the truth of statements; when used with [[Bayes theorem]], it ...
2: ...om events according to their relative frequencies of occurrence.
3: The Bayesian interpretation of probability allows probabilities assigned to random events,
4: ...the assignment of probabilities to any other kind of statement.
6: ...en a coin is tossed, only a Bayesian might assign probability 1/1000 to personal belief in the proposition that...

Statistical probability (475 bytes)
1: ...cy over a long series of events or the proportion of an event in a large population.
3: ...bility]], which have in common the application of probability to problems which don't necessarily involve repet...

Frequency probability (2045 bytes)
3: ...quency]] [[Probability interpretations|concept of probability]].
5: Most of the procedures commonly used to make statistical ...
7: ...l hypothesis testing]]. Other influential figures of the frequentist school include [[John Venn]], [[R...
9: ...ncept. The Bayesians supported the use of degrees of belief as a basis for statistical practice.
11: ...f you perform the experiment enough times, is the probability.

Inverse probability (736 bytes)
1: ...bsolete 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]]

Eclectic probability (1087 bytes)
1: ...ena which obey the [[probability axioms|axioms of probability theory]] as a reasonable interpretation. Sometime...
3: ...ior information, and a personal interpretation of probability for dealing with epistemic uncertainty, all witho...

Appeal to probability (1039 bytes)
1: ...rrespective of how unlikely it is. The fallacy is often used to exploit paranoia.
6: ...ver Intel's position, and eventually put them out of business altogether."
9: ...guments, enough for many to consider it a fallacy of itself.

Algorithmic probability (1492 bytes)
1: ...lomonoff]] invented the concept of '''algorithmic probability'''.
6: The algorithmic probability of any given finite output
7: prefix q is the sum of the probabilities of the programs that
9: programs have high probability.
11: Algorithmic probability is the main ingredient

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