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

of total expectation, the law of iterated expectations (LIE), Adam's law, the tower rule, and the smoothing property of conditional expectation, among other...

varies around its conditional mean E ⁡ [ Y ∣ X ] . {\displaystyle \operatorname {E} [Y\mid X].} Taking the expectation of this conditional variance across...

f_{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 ] Pr ( X > k )...

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

quantity used in place of the true conditional probability (or conditional expectation) underlying the proof. Raghavan gives this description: We first...

(X_{1}\mid X_{2}=x_{2})=1-\rho ^{2};} thus the conditional variance does not depend on x2. The conditional expectation of X1 given that X2 is smaller/bigger than...

observations, is equal to the most recent value. In other words, the conditional expectation of the next value, given the past, is equal to the present value...

the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization...

linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the...

derivative identity can be established between the conditional cumulant and the conditional expectation. For example, suppose that Y = X + Z where Z is standard...

{\displaystyle E[X_{t+j}|\Omega _{t}]=E_{t}[X_{t+j}].} With these time-dependent conditional expectations, there is the need to distinguish between the backshift...

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

the imputed complete data". Expectation conditional maximization (ECM) replaces each M step with a sequence of conditional maximization (CM) steps in which...

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...

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

distribution then the expected shortfall is equivalent to the tail conditional expectation defined by TCE α ⁡ ( X ) = E [ − X ∣ X ≤ − VaR α ⁡ ( X ) ] {\displaystyle...

In mathematics, non-commutative conditional expectation is a generalization of the notion of conditional expectation in classical probability. The space...

infinity. The conditional expectation of the limit inferior might not be well defined on this set, because the conditional expectation of the negative...

K\Rightarrow Y\perp \!\!\!\perp X\mid K} . Graphoid Conditional dependence de Finetti's theorem Conditional expectation To see that this is the case, one needs to...

that if g(X) is any kind of estimator of a parameter θ, then the conditional expectation of g(X) given T(X), where T is a sufficient statistic, is typically...

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...

several specific types of mathematical relationship between the conditional expectation of one variable given the other is not constant as the conditioning...

the conditional probability of failure is at most the conditional expectation of F {\displaystyle F} . Next we calculate the conditional expectation of...

[X\mid Y])+\operatorname {Var} (\operatorname {E} [X\mid Y]).} The conditional expectation E ⁡ ( X ∣ Y ) {\displaystyle \operatorname {E} (X\mid Y)} of X...

irrespective of other possible values of X. Given that X = 1, the conditional expectation of the random variable Y is E ( Y | X = 1 ) = 3 10 {\displaystyle...

capital, backtesting, stress testing, expected shortfall, and tail conditional expectation. Common parameters for VaR are 1% and 5% probabilities and one...

theorem – Conditional independence of exchangeable observations Conditional expectation – Expected value of a random variable given that certain conditions...

zero–one law Conditional probability Conditioning (probability) Conditional expectation Conditional probability distribution Regular conditional probability...

is used in order to create the conditional expectation and, similar to the ARIMA method, the conditional expectation is then compared to the account...