Chapter Seven

Random Vectors in

# 7.1 Introduction/Purpose of the Chapter

Often, we have more than one random variable describing the same object. For example, height and weight of a person are two different random variables. Each of the variables may be considered separately; but usually they have probabilistic ties, which means they have to be studied jointly. There is only one case where considering variables separately or jointly is identical: the case of independent variables. In probability theory, a random vector is any finite collection of real-valued random variables. More precisely, a random vector is a measurable function . It is usually denoted by

where each component is one-dimensional. A random vector is sometimes called a multidimensional random variable. The X_{i}, i = 1, …, N, are the components of the vector X. Each component is a random variable from Ω to .

# 7.2 Vignette/Historical Notes

The study of random vectors is very important today. In the big data studies we deal with many characteristics measures for each individual. In statistics the study of these vectors is ...