5 мая 2017 г. · Independent random variables are uncorrelated. In general, uncorrelated random variables need not be independent. But in specific examples they ...

11 апр. 2020 г. · In general, Cov[X,Y]=E[(X−E[X])(Y−E[Y])]=E[XY]−E[X]E[Y] is the covariance. And. in general, Var[X+Y]=Var[X]+Var[Y]+2Cov[X,Y] is the variance ...

7 окт. 2020 г. · Is there any counterexample to show that X,Y are two random variables and E(X∣Y)=E(X), but X and Y are not independent. Related. 0.

29 окт. 2015 г. · Independence implies uncorrelation. We say that two random variables are uncorrelated if E[XY]=E[X]E[Y]. If X and Y are independent and ...

3 апр. 2013 г. · I understand this would be simple if X and Y were independent however, I believe they are not since V(X)+V(Y)≠8. Find E(XY) with E(X)=4,E(Y)=10, ...

10 дек. 2020 г. · Since E(XY)−E(X)E(Y) doesn't change if you add a constant to one or both of X,Y, any dependent X,Y with E(XY)=E(X)E(Y)=0 can be shifted (thereby ...

14 дек. 2013 г. · If E(XY)=E(X)E(Y), then X and Y are uncorrelated, but not necessarily independent. – André Nicolas. Commented Dec 14, 2013 at 4:35.

29 янв. 2019 г. · If the two variables are independent, then E[Y|X]=E[Y]; that is, E[Y] is independent of X. Thus, E[XY]conditionalprobability=E[XE[Y|X] ...

18 нояб. 2017 г. · But if X and Y are independent, E[Y∣X]=E[Y] and thus the identity follows. – Sangchul Lee. Commented Nov 19, 2017 at 0:14.

14 дек. 2018 г. · See the following post: Is there any counterexample to show that X,Y are two random variables and E(X∣Y)=E(X), but X and Y are not independent.