Proving X=Y with Conditional Expectation

yavanna
Messages
10
Reaction score
0
How can I do this?

Let X,Y r.v., \mathbb{E}(X|Y)=Y and \mathbb{E}(Y|X)=X.
Proove that X=Y a.s.
 
Last edited:
Physics news on Phys.org
yavanna said:
How can I do this?

Let X,Y r.v., \mathbb{E}(X|Y)=Y and \mathbb{E}(Y|X)=X.
Proove that X=Y a.s.

could you give the definition of \mathbb{E}(X|Y) then it might be easier
 

Thread 'Here's a Statistics problem for game of Polo (or Hockey if you like)'

Namaste & G'day Postulate: A strongly-knit team wins on average over a less knit one Fundamentals: - Two teams face off with 4 players each - A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest) I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players. Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that...
View full post »

Thread 'Roulette wheel physics and probability'

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
View full post »

Similar threads

I Is this conditional expectation identity true?
Replies
1
Views
2K
I Help understanding conditional expectation identity
Replies
1
Views
2K
I Statistical modeling and relationship between random variables
Replies
7
Views
2K
I Expected value of X~Geom(p) given X+Y=z
Replies
5
Views
2K
I On Jensen's inequality for conditional expectation
Replies
1
Views
2K
I Proof request for best linear predictor
Replies
1
Views
2K
I How to obtain moment bound from the importance sampling identity?
Replies
1
Views
2K
I Sampling theory and random sample
Replies
5
Views
2K
MHB How to calculate conditional expectation E[g(x) | x>= Q] for x ~ exp(1)
Replies
2
Views
2K
I On pdf of a sum of two r.v.s and differentiating under the integral
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top