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...rred. Usually this is written as <math>P(A\mid B)</math>. This is read as "probability of A given B". The two events need not be related. They also need not occur ...the probability of B occurring. As a division by zero is not defined, the probability of B occurring must not be zero. ...

...to model the number of trials needed to obtain a first success, where the probability of success of each trial is <math>p</math>.<ref>{{cite web|title=11.1 - Geo [[Category:Probability distributions]] ...

...bility of a [[hypothesis]] given some observed pieces of evidence, and the probability of that evidence given the hypothesis. This theorem is named after [[Thomas * P(''A'') is the [[prior probability]] or [[marginal probability]] of ''A''. It is "prior" in the sense that it does not take into account a ...

...s occurring, it assumes that if one event occurs, this does not change the probability of the other events occurring. ...vely, <math>A</math> and <math>B</math> are independent precisely when the probability of them occurring together is equal to the [[Product (mathematics)|product] ...

...9-12|website=Math Vault|language=en-US}}</ref> It is used in [[probability theory]] and [[statistics]]. It is named after a [[Switzerland|Swiss]] scientist [ This distribution has only one [[parameter]], the probability of a success (''p''). In fact, Bernoulli distribution is the [[binomial dis ...

...on.</ref><ref>Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (1993). Probability and statistics for engineers and scientists (Vol. 5). New York: Macmillan.< For example, using probability, one can show that by throwing a coin up in the air and letting it land, ha ...

...d Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-09-14|website=Math Vault|language=en-U ...v}}</ref> It is useful, because it is relatively easy to show that certain probability distributions come close to it, under certain conditions. One of these cond ...

...d Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-10-13|website=Math Vault|language=en-U * [[Probability]] ...

...m]]s about the limiting behaviors of aggregated [[Probability distribution|probability distributions]]. They say that given a large number of independent [[random ...Pólya]] written in 1920, ''About the Central Limit Theorem in Probability Theory and the [[Moment (mathematics)|Moment]] problem''.<ref>[http://jeff560.trip ...

...hich definitely terminates but with a result that is only correct with the probability <math>p<1</math>). The algorithm [[gambling|gambles]] with the [[resource] [[Category:Game theory]] ...

A '''random variable''' is used in [[mathematics]] to study [[probability theory]]. It was developed to model the chance of events happening in all kinds of ...d Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-08-21|website=Math Vault|language=en-U ...

{{Information theory}} ...information, the [[probability]] (chance) of all possible events, and the probability of them happening at the same time, is needed. For example, to measure mutu ...

...d Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-08-21|website=Math Vault|language=en-U ...e formula <math>\sum_x x P(X=x) </math>, where <math>P(X=x) </math> is the probability that <math>X </math> equals <math>x </math>, and <math>x </math> ranges ove ...

[[File:Gumbel-Density.svg|thumb|260px|Gumbel probability distribution function (PDF)]] The '''Gumbel distribution''' is a [[probability distribution]] of extreme values. ...

...nics is the [[Heisenberg uncertainty principle]].<ref name=hofstra /> This theory is the idea that it's impossible to know both where something is and its [[ == Probability waves == ...

{{Hide in print|1={{Probability distribution In [[statistics]] the '''Maxwell–Boltzmann distribution''' is a particular [[probability distribution]] named after [[James Clerk Maxwell]] and [[Ludwig Boltzmann]] ...

...ame=Normal|type=density|pdf_image=[[File:Normal distribution pdf.png|325px|Probability density function for the normal distribution]]<br /><small>The green line i ...d Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-08-15|website=Math Vault|language=en-U ...

...is an important to [[statistics]], [[mathematical statistics]], [[decision theory]], and [[sequential analysis]]. Bayesian inference is used in [[science]], ...se. The figures denote the cells of the table involved in each metric, the probability being the fraction of each figure that is shaded. This shows that P(A<nowik ...

In [[probability theory]] and [[statistics]], the '''variance''' is a way to measure how far a [[se ...d Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-09-11|website=Math Vault|language=en-U ...

...d Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-09-10|website=Math Vault|language=en-U [[Category:Number theory]] ...