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t. e. 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.
hide. In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a ...
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.
Bayes' theorem is named after the Reverend Thomas Bayes(/beɪz/), also a statistician and philosopher. Bayes used conditional probability to provide an algorithm (his Proposition 9) that uses evidence to calculate limits on an unknown parameter. His work was published in 1763 as An Essay Towards Solving a Problem in the Doctrine of Chances.
Conditioning (probability) Beliefs depend on the available information. This idea is formalized in probability theory by conditioning. Conditional probabilities, conditional expectations, and conditional probability distributions are treated on three levels: discrete probabilities, probability density functions, and measure theory.
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events , hence the name.
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. This rule allows you to express a joint probability in ...
Conditional probability table. 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 ...
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