query: Does E(X|Y)=E(X) implies independence between X and Y?
positive_passages.docid: 154091
positive_passages.text: Is there any counterexample to show that $X,Y$ are two random variables and $E(X\mid Y)=E(X)$, but $X$ and $Y$ are not independent.
negative_passages.docid: 63218
negative_passages.text: Is conditional expectation with respect to two sigma algebra exchangeable?
negative_passages.docid: 133833
negative_passages.text: If $E(Y\mid X)$ is constant then $X, Y$ are uncorrelated.
negative_passages.docid: 155228
negative_passages.text: $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
negative_passages.docid: 138798
negative_passages.text: Independence and conditional distribution
negative_passages.docid: 5350
negative_passages.text: Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
negative_passages.docid: 135641
negative_passages.text: Algebraic independence of exponentials
negative_passages.docid: 38461
negative_passages.text: If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?
negative_passages.docid: 9665
negative_passages.text: Proof of the independence of the sample mean and sample variance
negative_passages.docid: 85818
negative_passages.text: $E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
negative_passages.docid: 20571
negative_passages.text: In a monoid, does $x \cdot y=e$ imply $y \cdot x=e$?
negative_passages.docid: 29339
negative_passages.text: Are functions of independent variables also independent?
negative_passages.docid: 140988
negative_passages.text: Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
negative_passages.docid: 95084
negative_passages.text: What is the expected value of $\min\{|X|,|Y|\}/\max\{|X|,|Y|\}$ assuming $X$ and $Y$ are independent?
negative_passages.docid: 121422
negative_passages.text: Independence between a constant random variable and another random variable.
negative_passages.docid: 92054
negative_passages.text: $X$ and $Y$ i.i.d., $X+Y$ and $X-Y$ independent, $\mathbb{E}(X)=0 $ and $\mathbb{E}(X^2)=1$. Show $X \sim N(0,1)$
negative_passages.docid: 134696
negative_passages.text: How can I show that the conditional expectation $E(X\mid X)=X$?