## Coupling of two non-independent random variables [closed]

Hi,

I have two random variables which are not independent. I know that, it is impossible to find the coupling of two r.v in general case, but I want to know if there exits some methods for special cases or not?

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 This is an extremely vague question, making it hard to produce a satisfying answer (see mathoverflow.net/howtoask#specific). What are you actually trying to do? If you just want to learn about coupling in general, have a look at a book (like books.google.com/…). If you have a more focused question, please edit your question and flag it for moderator attention asking to reopen. – Anton Geraschenko♦ Feb 11 2010 at 15:53 As a matter of fact I have marginal distributions of two r.v. X and Y. X=X_1+...+X_n where X_i's are independent exponentially r.v with parameters lambda_i, and Y=Y_1+...+Y_n where Y_i's are independent exponentially r.v.'s with parameters lambda_i. But the point is that X and Y are not independent. Is it possible to find the joint probability density function of X and Y in this case? – Simon Apr 8 2010 at 12:06