Hello,

I have a question regarding one of my homework problems about the joint CDF.

The question is:

If Fx,Y (x,y)={ (1-exp(-2x))(1-exp(-2y)). , x>=0 , y >=0
{ 0 , Otherwise



Find the probability p(X>x , Y>y)?

 

Can I say that p(X>0,Y>0) is equal to 1-p(X<=0,Y<=0)?

 

Can I say that p(X>0,Y>0) is equal to 1-p(X<=0,Y<=0)?

Only if the two regions are disjoint (no overlap) and, combined, cover the entire space. So ask yourself if there are any combinations of x and y that either fall into both areas or don't fall in either. If the answer to either question is yes, then you can't use that relationship.