query: Why do E(X|Y)=Y and E(Y|X)=X imply P(X=Y)=1?
positive_passages.docid: 662
positive_passages.text: If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely
negative_passages.docid: 111088
negative_passages.text: Conditional probability, $E[E(X\mid Y)\mid Y,Z]=?$
negative_passages.docid: 152495
negative_passages.text: Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
negative_passages.docid: 124742
negative_passages.text: P(A|C)=P(A|B)*P(B|C)?
negative_passages.docid: 20571
negative_passages.text: In a monoid, does $x \cdot y=e$ imply $y \cdot x=e$?
negative_passages.docid: 113411
negative_passages.text: If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
negative_passages.docid: 141540
negative_passages.text: What is wrong with the following "proof" that $e=1$?
negative_passages.docid: 123844
negative_passages.text: conditional expectation: an implication
negative_passages.docid: 37371
negative_passages.text: Why is expected value of random variable equal to mean
negative_passages.docid: 33054
negative_passages.text: Given a joint density function, what is the conditional expectation $E[Y|x]$?
negative_passages.docid: 67394
negative_passages.text: How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
negative_passages.docid: 77938
negative_passages.text: How to prove that minimum of two exponential random variables is another exponential random variable?
negative_passages.docid: 26833
negative_passages.text: Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.
negative_passages.docid: 25361
negative_passages.text: Intuition behind the Definition of Conditional Probability (for 2 Events)
negative_passages.docid: 64856
negative_passages.text: Finding $E(X\mid X>Y)$ when $X,Y$ are i.i.d $U(0,1)$
negative_passages.docid: 101394
negative_passages.text: Please explain the logic behind $d(xy) = y(dx) + x(dy)$
negative_passages.docid: 154091
negative_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.