If $E(X|Y) = E(X)$ then $E(XY)=E(X)E(Y)$
133833
If $E(Y\mid X)$ is constant then $X, Y$ are uncorrelated.
74713
Show that for any natural numbers, if $S(x)=S(y)$ then $x=y$.
124742
P(A|C)=P(A|B)*P(B|C)?
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
42193
Show that $E(Y^p)=\int_{0}^{\infty}px^{p-1}P(Y\geq x)dx$
123844
conditional expectation: an implication
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
45143
Identify $E(X\mid X+Y)$ for $X$ and $Y$ independent and Poisson
95022
Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
31846
Does $\neg(x > y)$ imply that $y \geq x$?
98470
If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
100916
Finding $\mathrm{Cov}(X,Y)$ and $E(X\mid Y=y)$ given the joint density of $(X,Y)$
85076
Is it true that $d(x,Y)=d(x,y_0)$ for some $y_0 \in Y$ when $Y$ is closed?
91216
Question about Conditional Expectation
118195
How does one prove that $e$ exists?
25654
E[X| X>Y] for independent X, Y ~ N(0,1)
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x