Probability and Random Variables

doi:10.1117/3.467443.ch13

Book: Mathematical Techniques for Engineers and Scientists

Author(s): Larry C. Andrews, Ronald L. Phillips

Published: 2003

https://doi.org/10.1117/3.467443.ch13

Author Affiliations +

Abstract

The objective of this chapter is to provide an overview of probability theory that is useful in physical applications. In particular, the theory presented here makes it possible to mathematically describe or model random signals that arise, for example, in the analysis of communication systems. Such random signals, called random processes, are discussed in further detail in Chapter 14. The mathematical theory developed in basic courses in engineering and the physical sciences is usually based on deterministic phenomena. As an example, the input to a linear filter is often presumed to be a deterministic quantity, such as a sine wave, step function, impulse function, and so on, leading to a deterministic output. However, in practice the input to a filter may contain a fluctuating or "random" quantity (noise) that yields some uncertainty about the output. In general, an unpredictable noise signal always appears at the input to any communication receiver and thus interferes with the reception of incoming radio or radar "signals." Situations like this that involve uncertainty or randomness in some form cannot be analyzed by deterministic methods but must be treated by probabilistic methods. Probability theory has become an indispensable tool in engineering and scientific analysis involving electron emission, radar detection, quality control, statistical mechanics, turbulence, and noise, among other areas.