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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 ...
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
To do this, instead of computing the conditional probability of failure, the algorithm computes the conditional expectation of Q and proceeds accordingly: at each interior node, there is some child whose conditional expectation is at most (at least) the node's conditional expectation; the algorithm moves from the current node to such a child ...
Note: The conditional expected values E( X | Z) and E( Y | Z) are random variables whose values depend on the value of Z. Note that the conditional expected value of X given the event Z = z is a function of z. If we write E( X | Z = z) = g(z) then the random variable E( X | Z) is g(Z). Similar comments apply to the conditional covariance.
Assumption implies that the conditional expectation of X n given F n–1 equals E[X n] almost surely for every n ∈ , hence (M n) n∈ 0 is a martingale with respect to the filtration (F n) n∈ 0 by assumption .
In statistics, kernel regression is a non-parametric technique to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables X and Y .
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 .
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 ).