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Random vectors. Fix a positive integer n. We say a subset R of Rn
 

Summary: Random vectors.
Fix a positive integer n. We say a subset R of Rn
is a rectangle if it it the n-fold Cartesian product
of intervals of real numbers.
Definition. Suppose (S, E, P) We say
X : S Rn
is a random vector if
{X R} E whenever R is a rectangle.
Suppose X is a random vector. Its (joint) cumulative distribution function
FX : Rn
[0, 1]
is defined by
FX(x) = P(X1 x1, . . . , Xn xn) for x Rn
.
We say X is discrete if
xRn
P(X = x) = 1
in which case its (joint) probability mass function
pX : Rn
[0, 1]

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics