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If the conditional distribution of given is a continuous distribution, then its probability density function is known as the conditional density function. [1] The properties of a conditional distribution, such as the moments , are often referred to by corresponding names such as the conditional mean and conditional variance .
The unconditional expectation of rainfall for an unspecified day is the average of the rainfall amounts for those 3652 days. The conditional expectation of rainfall for an otherwise unspecified day known to be (conditional on being) in the month of March, is the average of daily rainfall over all 310 days of the ten–year period that fall in ...
First, the question is asked on the given formula Φ. If the answer is "no", the formula is unsatisfiable. Otherwise, the question is asked on the partly instantiated formula Φ{x 1 =TRUE}, that is, Φ with the first variable x 1 replaced by TRUE, and simplified accordingly. If the answer is "yes", then x 1 =TRUE, otherwise x 1 =FALSE. Values ...
The variance of the conditional mean, ( []), measures how much these conditional means differ (i.e. the “explained” or between-group part). Adding these components yields the total variance Var ( Y ) {\displaystyle \operatorname {Var} (Y)} , mirroring how analysis of variance partitions variation.
The material conditional (also known as material implication) is an operation commonly used in logic.When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false.
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.
While not itself a conditional function, it is often used inside of those functions, so it is briefly described here. See Manual:Expr parser function syntax for further details. {{#expr: expression}} Unlike the #if function, all values in the expression evaluated by #expr are assumed to be numerical. It does not work with arbitrary strings.
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.