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In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. [1] This particular method relies on event A occurring with some sort of relationship with another event B.
Given , the Radon-Nikodym theorem implies that there is [3] a -measurable random variable ():, called the conditional probability, such that () = for every , and such a random variable is uniquely defined up to sets of probability zero. A conditional probability is called regular if () is a probability measure on (,) for all a.e.
Conditional probabilities, conditional expectations, and conditional probability distributions are treated on three levels: discrete probabilities, probability density functions, and measure theory. Conditioning leads to a non-random result if the condition is completely specified; otherwise, if the condition is left random, the result of ...
In probability theory, the Borel–Kolmogorov paradox (sometimes known as Borel's paradox) is a paradox relating to conditional probability with respect to an event of probability zero (also known as a null set). It is named after Émile Borel and Andrey Kolmogorov.
Pages in category "Conditional probability" The following 13 pages are in this category, out of 13 total. This list may not reflect recent changes. ...
Independently of Bayes, Pierre-Simon Laplace used conditional probability to formulate the relation of an updated posterior probability from a prior probability, given evidence. He reproduced and extended Bayes's results in 1774, apparently unaware of Bayes's work, in 1774, and summarized his results in Théorie analytique des probabilités (1812).
In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables).
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