November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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4.6 RANDOM VECTORS
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) 
where is the random vector. An example mapping for N = 2 is shown ...
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