The definition of a random variable can be extended to a random vector by considering multiple mappings (functions) of outcomes in the event space to N-dimensional Euclidean space . Let the mappings be denoted by the column vector of functions , where maps to the nth coordinate of . Thus, instead of open intervals in the case of a single (one-dimensional) mapping to , the vector mapping is a generalization such that events map to open hyper-rectangles in . The notation can be simplified as follows:

(4.48) Numbered Display Equation

where is the random vector. An example mapping for N = 2 is shown ...

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