19 сент. 2020 г. · The conditional expectation E(Y|X) can be interpreted as projection of random variable Y onto random variable X.

16 окт. 2019 г. · A situation arises in which the value of a random variable X is observed and then, on the basis of the observed value, an attempt is made to predict the value ...

15 мая 2024 г. · The conditional expectation E[X∣Y] gives us some new random variable h(Y) that is the orthogonal projection of X onto σ(Y), the sigma algebra of ...

11 янв. 2019 г. · I'm reading a paper in which the expected value of a random variable, E[X], is characterized as an orthogonal projection. This is on page 10.

4 окт. 2013 г. · The problem now is this: given X,Y∈L2(Ω,F,μ), find the projection of Y onto the subspace L2(Ω,FX,μ), where FX is the σ-subalgebra of F generated ...

18 авг. 2016 г. · The conditional expectation of a random variable is an entirely different quantity from the expectation of the same random variable, i.e., E[ξ|G] ...

11 нояб. 2013 г. · We use conditional expectation because we expect there to be a relationship between a predictor variable and the response variable.

26 нояб. 2016 г. · The conditional expectation (which is the best predictor in mean-squared error sense) will be a linear function of the conditioning variables.

30 мая 2023 г. · The conditional expectation is the orthogonal projection on the space of (equivalence classes of) X-measurable rvs (ie, functions of X because of factorization ...

21 мар. 2021 г. · I'm having a little trouble deriving the formula for Var[X|Y]=E[X2|Y]−E[X|Y]2. Particularly, when expanding the squared expression E[(Y−E(Y|X))2 ...