In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated...

{\mathcal {G}})\;} An expectation of a random variable with respect to a regular conditional probability is equal to its conditional expectation. Consider the...

component is the expectation of the conditional variance; the other two components are the variance of the conditional expectation. Let ( x 1 , y 1 )...

[X\mid {\mathcal {G}}_{1}]\quad {\text{(a.s.)}}.} Proof. Since a conditional expectation is a Radon–Nikodym derivative, verifying the following two properties...

tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the...

X ) {\displaystyle \operatorname {E} (Y\mid X)} stands for the conditional expectation of Y given X, which we may recall, is a random variable itself...

e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value...

is the conditional density of Y given X. This result can be extended to measure theoretical conditional expectation using the regular conditional probability...

}xf_{X}(x\mid X>k)\,dx.} Alternatively, by using the definition of conditional expectation, it can be written as g ( k ) = E ⁡ [ X ∣ X > k ] P ( X > k ) {\displaystyle...

that is common knowledge at time t (this is often subscripted below the expectation operator); then the expected value of the realisation of X, j time-steps...