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  2. Conditional probability - Wikipedia

    en.wikipedia.org/wiki/Conditional_probability

    In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) [2] or occasionally P B (A).

  3. Conditional probability distribution - Wikipedia

    en.wikipedia.org/wiki/Conditional_probability...

    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.

  4. Conditional probability table - Wikipedia

    en.wikipedia.org/wiki/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 other variables).

  5. Chain rule (probability) - Wikipedia

    en.wikipedia.org/wiki/Chain_rule_(probability)

    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.

  6. Conditioning (probability) - Wikipedia

    en.wikipedia.org/wiki/Conditioning_(probability)

    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 ...

  7. Conditional expectation - Wikipedia

    en.wikipedia.org/wiki/Conditional_expectation

    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 subset of ...

  8. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    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.

  9. Posterior probability - Wikipedia

    en.wikipedia.org/wiki/Posterior_probability

    In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest ...

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