Is it true that if $E(X\mid Y)=Y$ and $E(Y\mid X)=X$, then $X$ equals $Y$?
662
If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
26833
Prove that $\mathbb P(X>Y) =\frac{b}{a + b}$ if $X, Y$ are exponentially distributed with parameters $a$ and $b$.
83464
Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
132392
Properties of Expectation
123555
Proving that if $ab=e$ then $ba=e$
72906
Is $\frac{\partial}{\partial x_1}=\frac{\partial}{\partial y_1}$ if $x_1=y_1$?
95022
Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
37371
Why is expected value of random variable equal to mean
33054
Given a joint density function, what is the conditional expectation $E[Y|x]$?
107058
Prove that $E(X\ln X)\le E X E\ln X$
152310
If $E$ has Lebesgue measure $0$, must there exist a translate such that $E\cap E+x=\varnothing$?
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
57938
When do two functions become equal?
45143
Identify $E(X\mid X+Y)$ for $X$ and $Y$ independent and Poisson
113778
Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.
157920
Can I define $y=y(x)$?