Probability and Random Processes an Introduction for Applied Scientists and Engineers
A post-calculus approach to this important mathematical discipline. A cursory survey of engineering reveals the widespread application of probability theory. Such diverse fields as systems analysis, decision theory, statistics, automatic control, modern management, and cybernetics all rely on a probabilistic approach. Chalkboard photographs from all the videocassettes are provided in the lecture notes. A mathematics pretest is provided to determine proficiency in calculus concepts and techniques used in the video course. The video course Random processes is a follow-on to this course.
Why Read This Book
You should read this book to get a compact, engineering-focused grounding in probability and random processes that directly supports statistical signal-processing tasks (spectral analysis, filtering, detection). It emphasizes intuition and applied examples more than measure-theoretic formalism, so you can quickly connect probabilistic ideas to signal-processing problems.
Who Will Benefit
Engineers and graduate students who need a practical introduction to probability and random processes to support work in DSP, communications, radar, or control.
Level: Intermediate — Prerequisites: Single-variable calculus (integration and differentiation), basic linear algebra, and familiarity with elementary signals & systems concepts; comfort with complex numbers and basic transforms is helpful.
Key Takeaways
- Explain the axioms of probability and work with discrete and continuous random variables and their distributions
- Compute expectations, moments, and conditional statistics for single and joint random variables
- Characterize random processes (stationarity, ergodicity, correlation) and derive autocorrelation and cross-correlation functions
- Relate correlation functions to power spectral densities and apply the Wiener–Khinchin relationships
- Analyze the response of linear systems to random inputs and apply basic ideas of optimal linear estimation
- Use limit theorems (law of large numbers, central limit theorem) and characteristic functions for practical approximations
Topics Covered
- 1. Introduction and the Role of Probability in Engineering
- 2. Basic Probability Concepts and Axioms
- 3. Discrete and Continuous Random Variables
- 4. Joint Distributions and Conditional Probability
- 5. Expectation, Moments, and Transform Methods
- 6. Characteristic Functions and Limit Theorems
- 7. Introduction to Stochastic Processes
- 8. Stationarity, Ergodicity, and Statistical Descriptions
- 9. Correlation Functions and Power Spectral Density
- 10. Linear Systems Driven by Random Inputs
- 11. Gaussian and Poisson Processes
- 12. Markov Processes and Simple Stochastic Models
- 13. Introductory Detection/Estimation Remarks and Applications
How It Compares
Covers much of the same foundational ground as A. Papoulis' 'Probability, Random Variables, and Stochastic Processes' and Alberto Leon-Garcia's texts, but is more compact and applied in style and older in presentation.
