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2.4.4 Bivariate Probability Distributions     continued...

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: