Let $X$ and $Y$ be square integrable random variables s.t. $E[X|Y]=Y$ and $E[Y|X]=X$. Prove $P(X=Y)=1$.
662
If $E[X|Y]=Y$ almost surely and $E[Y|X]=X$ almost surely then $X=Y$ almost surely
101754
Transformation of Random Variable $Y = X^2$
23946
Prove the definitions of $e$ to be equivalent
40078
Calculate $E(Y)$ and $Var(Y)$ given the random variable which is exponentially distributed
81973
Definition of $d (P (x ,y )dx)$
62665
If X and Y are continuous random variables, then the random vector (X,Y) is a continuous random vector?
89544
Expectation of a random variable that takes points in the natural numbers
144359
A random variable that induces a $\sigma$-algebra the same as the one in the sample space
46865
Proof of linearity for expectation given random variables are dependent
23765
Prove that lebesgue integrable equal lebesgue measure
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
136707
Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution
116975
Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
149362
Prove that $ \mathbb{E}[XY] - \mathbb{E}[X] \mathbb{E}[Y] = \int_{- \infty}^\infty \int_{- \infty}^\infty (F(x,y)-F_X(x) F_Y(y)) \,dx\,dy,$
34916
Conditional expectation equals random variable almost sure
99024
Let $\,E=\{(x,y) \in \Bbb R^2: |x| \le 1,|y|\le 1\}.$