Random Quantities and Random Vectors

Abstract

By definition, values of random signals at a given sampling time are random quantities which can be distributed over a certain range of values. The tools for the precise, quantitative description of those distributions are provided by the classical probability theory. However natural, its development has to be handled with care since the overly heuristic approach can easily lead to apparent paradoxes. 10 But the basic intuitive idea that for independently repeated experiments, probabilities of their particular outcomes correspond to their relative frequencies of appearance, is correct. Although the concept of probability is more elementary than the concept of cumulative probability distribution functions, we assume that the reader is familiar with the former at the high school level, and start our exposition with the latter, which not only applies universally to all types of data, both discrete and continuous, but also gives us a tool to immediately introduce the probability calculus ideas, including the physically appealing probability density function.