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

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

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

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...

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

(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...

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...

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

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

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...

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...

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

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

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

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...

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

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...

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

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

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

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...

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...

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

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

headings zero conditional, first conditional (or conditional I), second conditional (or conditional II), third conditional (or conditional III) and mixed...

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

observation (the so-called selection equation) together with the conditional expectation of the dependent variable (the so-called outcome equation). The...

Conditional expectation – Expected value of a random variable given that certain conditions are known to occur Borel–Kolmogorov paradox – Conditional...