how can I calculate this joint distribution

Suppose that one object has two properties, and they are two discrete variable, as X and Y. The population number of both X and Y are the same. For example, there are N samples of X and Y either. I want to calculate a joint distribution like the equation below

Is p the ratio of the number of (X,Y), where 0<=X<=X1 and 0<=Y<=Y1, and the total number of (X,Y)? Anyone helps? Thanks.