The quantity is called the * conditional* pdf.
The constraint that simply means that the r.v.'s and
are * not mutually exclusive*, meaning there
is some probability that both and will occur together.
Note that if **x** and **y** are independent r.v.'s, then and
reduce to the univariate pdf's for **x** and **y**:

and therefore for independent pdf's we find that the bivariate pdf is simply the product of the two univariate pdf's: