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Constructive proof for a problem of discrete random variables.

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The problem is:

For two discrete random variables $X$, $Y sim p(x,y)$, can we find another random variable $Z$ independent of $X$, such that there exists a function $f$ satisfying $Y = f(X,Z)$?

I've got the hint that a constructive proof is needed, but I still have no idea about how to do the proof.

probability-distributions random-variables constructive-mathematics

share|cite|improve this question

edited Mar 17 at 10:42

Rócherz

3,0013821

asked Mar 16 at 9:19

Keith NullKeith Null

1

$endgroup$

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  $begingroup$
  Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
  $endgroup$
  – José Carlos Santos
  Mar 16 at 9:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Posts that consist only of a problem statement are discouraged on this site. Please expand your post by including the source, background, and motivation of the problem, and your thoughts on methods to solve it. When you asked the question, a link was provided to this page, which has useful advice: How to ask a good question
  $endgroup$
  – Carl Mummert
  Mar 16 at 13:33
  

  
  
  
  

add a comment | 

0

1

$begingroup$

The problem is:

For two discrete random variables $X$, $Y sim p(x,y)$, can we find another random variable $Z$ independent of $X$, such that there exists a function $f$ satisfying $Y = f(X,Z)$?

I've got the hint that a constructive proof is needed, but I still have no idea about how to do the proof.

probability-distributions random-variables constructive-mathematics

share|cite|improve this question

edited Mar 17 at 10:42

Rócherz

3,0013821

asked Mar 16 at 9:19

Keith NullKeith Null

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
  $endgroup$
  – José Carlos Santos
  Mar 16 at 9:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Posts that consist only of a problem statement are discouraged on this site. Please expand your post by including the source, background, and motivation of the problem, and your thoughts on methods to solve it. When you asked the question, a link was provided to this page, which has useful advice: How to ask a good question
  $endgroup$
  – Carl Mummert
  Mar 16 at 13:33
  

  
  
  
  

add a comment | 

$begingroup$

The problem is:

For two discrete random variables $X$, $Y sim p(x,y)$, can we find another random variable $Z$ independent of $X$, such that there exists a function $f$ satisfying $Y = f(X,Z)$?

I've got the hint that a constructive proof is needed, but I still have no idea about how to do the proof.

probability-distributions random-variables constructive-mathematics

share|cite|improve this question

edited Mar 17 at 10:42

Rócherz

3,0013821

asked Mar 16 at 9:19

Keith NullKeith Null

1

$endgroup$

share|cite|improve this question

edited Mar 17 at 10:42

Rócherz

3,0013821

asked Mar 16 at 9:19

Keith NullKeith Null

1

share|cite|improve this question

edited Mar 17 at 10:42

Rócherz

3,0013821

asked Mar 16 at 9:19

Keith NullKeith Null

1

edited Mar 17 at 10:42

Rócherz

3,0013821

edited Mar 17 at 10:42

Rócherz

3,0013821

asked Mar 16 at 9:19

Keith NullKeith Null

1

asked Mar 16 at 9:19

Keith NullKeith Null

1