Sentence:  A two-dimensional <WSD>random variable</WSD> is a mapping of the points in the sample space to ordered pairs {"x", "y"}. Usually, when dealing with a pair of <WSD>random variables</WSD>, the sample space naturally partitions itself so that it can be viewed as a combination of two simpler sample spaces. 
Meaning of the word marked with <WSD> tags:  A measurable function from a sample space to the measurable space of possible values of the variable.