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Chapter 2
RANDOM VECTORS
AND THEIR PROPERTIES
In succeeding chapters, we often make use of the properties of random
vectors. We also freely employ standard results from linear algebra. This
chapter is a review of the basic properties of a random vector [1,2] and the
related techniques of linear algebra [3-5). The reader who is familiar with
these topics may omit this chapter, except for a quick reading to become fami-
liar with the notation.
2.1 Random Vectors and their Distributions
Distribution and Density Functions
As we discussed in Chapter 1, the input to a pattern recognition network
is a random vector with n variables as
x = [x,x* . . . X,]T ,
where T denotes the transpose of the vector.
Distribution function: A random vector may be characterized by a pr-o-
bahility distribution function, which is defined by
P(.Y,....,?c,l)=PI.~x, SX,, ..., x,, Ix,,] , (2.2)
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