5.2 Jointly distributed random variables

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5.2 Jointly distributed random variables

Suppose we have an experiment that has two or more random variables defined on its event space and we wish to form a random variable that takes into account each of the individual random variables. These are called jointly distributed random variables, and they represent the intersections of the individual random variable event spaces. Jointly distributed random variables are represented with the following notation:

(5.32) 

Stated simply, joint random variables derive their output from a function whose domain is the set of outcomes for all of the individual random variable domains.

It should be noted here that more complicated combinations and conditions for the random variable function may be constructed. For example, consider the following random variables:

(5.33) 

(5.34) 

(5.35) 

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