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**continuous**random vector (X,Y) with a joint density function

In order to check whether it is indeed a joint density ƒ(x,y) the method is to check if ∫∫ƒ(x,y)dxdy=1 where the integrals limits follow the bounds of x and y.

However, is it the case that if given an arbitrary

**discrete**random vector (X,Y) with a joint density function:

In order to check whether it is indeed a joint density ƒ(x,y) the method is to check if ∑∑ƒ(x,y)=1 where the summations are, given bounds, for all those x and y.

Or are they both the ∫∫ f(x,y)dxdy=1? I know further on for finding the expectation and such that

**discrete**uses the summation and

**continuous**takes the integral but not sure if it differs in the first step or why it does.