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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 ...
The statement "The probability that if , then , is 20%" means (put intuitively) that event may be expected to occur in 20% of the outcomes where event occurs. The standard formal expression of this is () =, where the conditional probability equals, by definition, () / ().
In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
Pages in category "Conditional probability" The following 13 pages are in this category, out of 13 total. This list may not reflect recent changes. ...
In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability distribution is a parametrized family of probability measures called a Markov kernel .
The conditional probability at any interior node is the average of the conditional probabilities of its children. The latter property is important because it implies that any interior node whose conditional probability is less than 1 has at least one child whose conditional probability is less than 1.
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