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I have two random variables [itex]X[/itex] and [itex]Y[/itex] that can take values of the kind [itex](a,b)[/itex] where [itex]a,b\in \{ 0,1,2,3 \}[/itex]. Thus, the sample space has only 16 elements.

I have, say,Nobservations for bothXandY, and I would like to know if there is some correlation betweenXandY.

- How is this typically done? Perhaps by calculating the mutual information betweenXandY?

- Should I treatXandYas2-dimensionalrandom variables? Or is it better to convert them to1-dimensionalrandom variables by using the mapping [itex](a,b)\longmapsto 4a+b[/itex] ?

In this way the sample space would simply become [itex]\{ 0,1,2,\ldots,15\}[/itex].

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# Question on random variables and histograms

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