An unusual joint probability density function

Hi all,

I have a problem that I'm not at all sure how to approach, and would appreciate any guidance on how to proceed (or if I can proceed at all). I have two discrete random variables, for which I know the probability of all possible (independent) outcomes, but I want to determine the joint pdf and the applicability of these independent probabilities becomes a little questionable.

For example, say:

P_{X}(A) = 0.16

P_{X}(B) = 0.11

P_{X}(C) = 0.07

...

and also that:

P_{Y}(A) = 0.12

P_{Y}(B) = 0.17

P_{Y}(C) = 0.09

...

The problem I have is to determine the probability of the outcomes of the joint pdf, **given that the combination of these two random variables must agree on the outcome**. So, P_{X,Y}(A,B) = P_{X,Y}(A,C) = P_{X,Y}(B,C) = 0, which obviously a little different from the typical outcome here.

I hope that makes some semblance of sense, and that some mathematics that I'm capable of understanding can be brought to bear on the problem (my suspicion is that a fundamental piece of information that would help solve the problem is not available). Any help would be appreciated.

Thanks,

Andy