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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).
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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.
The table below shows the output from a template call (we'll call the template {{Conditional tables/example 1}}) with different values for {{{variable_foo}}}: Template call Result
Part of a series on statistics: Probability theory; Probability. Axioms; Determinism. System; Indeterminism; Randomness; Probability space; Sample space; Event ...
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).
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 .
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