# Joint Probability/Mutual Information Normalization

1. Mar 3, 2010

### Nahtix

1. The problem statement, all variables and given/known data
Find the Corresponding normalization constants for the joint guassian

$$\\p\\(x,y) \alpha\ exp(-(ax^2/2) - (by^2/2) -cxy)$$

ie: find P(x), P(y), and P(X,Y) normalization constants

relevant equations:
Mutual Information: M(x,y)
$$\\M(x,y) = \sum\\p(x,y)ln(p(x,y)/(p(x)*p(y)))$$

3. The attempt at a solution
I've tried an integral over y then x but I end up with some messed up erf that I can't get rid of. My professor told me that the real point of this is that later we can use mutual information to get a ratio of the constants and that should equal $$\\1/2\\ln(1-c^2/ab)$$ but I haven't gotten anywhere close. I really just need a hint of where to start on this one as I have gotten nowhere with it any help is very appreciated.