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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).
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.
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 ...
For example, consider the task with coin flipping, but extended to n flips for large n. In the ideal case, given a partial state (a node in the tree), the conditional probability of failure (the label on the node) can be efficiently and exactly computed. (The example above is like this.)
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 ...
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.
The curve shows the estimated probability of passing an exam (binary dependent variable) versus hours studying (scalar independent variable). See § Example for worked details. In statistics , the logistic model (or logit model ) is a statistical model that models the log-odds of an event as a linear combination of one or more independent ...
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). For example ...