Search results
Results from the WOW.Com Content Network
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 ...
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 conditional expectation of X 1 given X 2 is ... In short, the probability density function (pdf) of a multivariate normal is = ...
Here, as usual, stands for the conditional expectation of Y given X, which we may recall, is a random variable itself (a function of X, determined up to probability one). As a result, Var ( Y ∣ X ) {\displaystyle \operatorname {Var} (Y\mid X)} itself is a random variable (and is a function of X ).
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 ...
A more general definition can be given in terms of conditional expectation. Consider a function : [,] satisfying (()) = [] for almost all . Then the conditional probability distribution is given by
Thus, we postulate that the conditional expectation of given is a simple linear function of , {} = +, where the measurement is a random vector, is a matrix and is a vector. This can be seen as the first order Taylor approximation of E { x ∣ y } {\displaystyle \operatorname {E} \{x\mid y\}} .
Conditional expectation; Expectation (epistemic) Expectile – related to expectations in a way analogous to that in which quantiles are related to medians; Law of total expectation – the expected value of the conditional expected value of X given Y is the same as the expected value of X; Median – indicated by in a drawing above