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  2. 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.

  3. 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).

  4. Chain rule (probability) - Wikipedia

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

    This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.

  5. 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 ...

  6. Conditioning (probability) - Wikipedia

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

    Conditional probability may be treated as a special case of conditional expectation. Namely, P ( A | X) = E ( Y | X) if Y is the indicator of A. Therefore the conditional probability also depends on the partition α X generated by X rather than on X itself; P ( A | g(X) ) = P (A | X) = P (A | α), α = α X = α g(X).

  7. Conditional mutual information - Wikipedia

    en.wikipedia.org/wiki/Conditional_mutual_information

    In probability theory, particularly information theory, the conditional mutual information [1] [2] is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.

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