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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. 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).

  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. This rule allows one to express a joint probability in terms ...

  6. 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).

  7. Chain rule for Kolmogorov complexity - Wikipedia

    en.wikipedia.org/wiki/Chain_rule_for_Kolmogorov...

    The chain rule [citation needed] for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states: (,) = + (|)That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.

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