Probability and Random Processes for Electrical and Computer Engineers
The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further resources for this title, including solutions (for instructors only), are available online at www.cambridge.org/9780521864701.
Why Read This Book
You will gain a rigorous, engineer-focused grounding in probability and random processes that directly supports analysis and design in communications, DSP, and radar. The text balances intuition, worked examples, and proofs so you can move from modeling noise and signals to applying spectral methods and limit theorems in real systems.
Who Will Benefit
Advanced undergraduate or graduate electrical/computer engineers and practicing signal-processing or communications engineers who need a compact, mathematically sound reference for probability and stochastic tools used in DSP, radar, and communications.
Level: Advanced — Prerequisites: Single-variable calculus, basic multivariable calculus, linear algebra, and an introductory course in elementary probability (discrete/continuous random variables and basic distributions). Familiarity with signals and systems is helpful but not required.
Key Takeaways
- Model stochastic signals and noise using random variables, random vectors, and random processes applicable to communications and radar
- Compute and manipulate distributions, moments, characteristic functions, and transform-domain representations for analysis
- Analyze stationary processes, autocorrelation, and power spectral density and apply spectral representations (Fourier/PSD) to linear systems
- Apply Gaussian random vector theory and conditional expectation to estimation and detection problems in signal processing
- Use limit theorems and modes of convergence to justify asymptotic approximations and performance bounds
- Analyze and apply Markov chains and basic stochastic stability concepts to communication protocols and signal models
Topics Covered
- 1. Probability Spaces and Axioms
- 2. Discrete and Continuous Random Variables
- 3. Expectation, Moments, and Inequalities
- 4. Transform Methods: MGFs and Characteristic Functions
- 5. Limit Theorems and Modes of Convergence
- 6. Random Vectors and Joint Distributions
- 7. Gaussian Random Vectors and Conditional Distributions
- 8. Random Processes: Definitions and Examples
- 9. Stationarity, Ergodicity, and Correlation Functions
- 10. Spectral Analysis and Power Spectral Density
- 11. Linear Systems Driven by Random Processes
- 12. Markov Chains and Discrete-Time Stochastic Models
- 13. Convergence of Random Processes and Advanced Topics
Languages, Platforms & Tools
How It Compares
Compared with Leon-Garcia's Probability and Random Processes (more example-driven and engineering-focused) and Papoulis & Pillai (more classical and mathematically encyclopedic), Gubner is concise and modern with clear links to communications and DSP applications.
