Chapter 1

Random Vectors

1.1. Definitions and general properties

Recalling that image the set of real n -tuples, can be fitted into two laws:

image

making it a vector space of dimension n .

The base implicitly considered on imagen will be the canonical base 1 =(1,0,…0),…,n =(0,…,0,1) and ximagen expressed in this base will be denoted:

image

Definition of a real random vector

Beginning with a basic definition, without concerning ourselves for the moment with its rigor: we can say simply that a real vector image : linked to a physical or biological phenomenon is random if the value taken by this vector is unknown, as long as the phenomenon is not completed.

For typographical reasons, the vector will instead be written XT =(X1,…,Xn) or even X = (X1,…,Xn) when there is no risk of confusion.

In other words, given a random vector X and B ⊂ n , we do not know if the assertion (also called the event) (X ∈ B) is true or ...

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