5 мая 2017 г. · Independent random variables are uncorrelated. In general, uncorrelated random variables need not be independent. But in specific examples they ... Can two random variables $X,Y$ be dependent and such that ... E[X]E[Y]$ affected if $X$ and $Y$ aren't independent random ... E(XY)=E(X)E(Y)≠0 implies independance Does E(X|Y)=E(X) implies independence between X and Y? Другие результаты с сайта math.stackexchange.com

3 окт. 2013 г. · Intuitively, it just throws me off to think that E(X+Y) = E(X) + E(Y), even if X and Y are not independent. All related (34). Recommended. How do I prove that E(x+y) = E(x) +E(y)? - Quora What is the expected value of X+Y when X and Y are discrete ... Другие результаты с сайта www.quora.com

If X and Y are independent, then E(XY ) = E(X)E(Y ). However, the converse is not generally true: it is possible for E(XY ) = E(X)E(Y ) even.

Продолжительность: 0:59
Опубликовано: 19 авг. 2022 г.

2 мар. 2019 г. · Once you condition on X, it is no longer random, so it can come out of the expectation: E(XY|X) = XE(Y|X) always.

13 мар. 2021 г. · The second part of the equality is always true provided the expected values exist even if X and Y are not independent because E[X+Y]=EX+EY.

As with the variance, Cov(X, Y ) = E(XY ) - (EX)(EY ). It follows that if X and Y are independent, then E(XY )=(EX)(EY ), and then Cov(X, Y )=0.

The fact that some two random variables are uncorrelated, ie, E(XY) = EX EY, does not imply that they are independent. Show that this is nevertheless true.

28 окт. 2023 г. · Page 22 of Chapter 4 mentions that we can find E[XY] for dependent random variables by using E[XY] = E[X]E[Y] + cov[X,Y].