Probability, Statistics, and Random Processes for Engineers
For courses in Probability and Random Processes.
Probability, Statistics, and Random Processes for Engineers, 4e is a useful text for electrical and computer engineers. This book is a comprehensive treatment of probability and random processes that, more than any other available source, combines rigor with accessibility. Beginning with the fundamentals of probability theory and requiring only college-level calculus, the book develops all the tools needed to understand more advanced topics such as random sequences, continuous-time random processes, and statistical signal processing. The book progresses at a leisurely pace, never assuming more knowledge than contained in the material already covered. Rigor is established by developing all results from the basic axioms and carefully defining and discussing such advanced notions as stochastic convergence, stochastic integrals and resolution of stochastic processes.
Why Read This Book
You will get a rigorous yet approachable grounding in probability and random processes tailored for engineering problems in DSP, communications, and radar. The book builds from first principles through statistical signal-processing tools so you can confidently analyze random signals, design estimators/detectors, and interpret spectral results in real systems.
Who Will Benefit
Upper‑level undergraduates, graduate students, and practicing electrical/computer engineers who need a solid probabilistic foundation for DSP, communications, radar, audio/speech, or statistical signal processing.
Level: Intermediate — Prerequisites: Single‑variable calculus, multivariable calculus (basic familiarity), and introductory linear algebra; some familiarity with basic signals and systems concepts is helpful but not required.
Key Takeaways
- Apply probability theory to model and analyze random variables and their joint behavior in engineering contexts
- Analyze discrete- and continuous-time random processes, including stationarity, ergodicity, autocorrelation, and power spectral density
- Derive and use linear estimation and detection rules (e.g., MMSE, least squares, MAP, Neyman–Pearson) for noisy measurements
- Perform spectral analysis using Fourier methods and understand the statistical properties of the FFT and periodogram
- Model and analyze key stochastic processes used in communications and radar (Gaussian, Poisson, Markov, and autoregressive processes)
- Design and assess adaptive filtering and linear systems driven by random inputs using covariance and frequency-domain methods
Topics Covered
- 1. Fundamentals of Probability
- 2. Random Variables and Probability Distributions
- 3. Joint Distributions and Transform Methods
- 4. Expectation, Moments, and Inequalities
- 5. Limit Theorems and Convergence Concepts
- 6. Random Sequences and Discrete-Time Processes
- 7. Stationarity, Ergodicity, and Correlation Functions
- 8. Power Spectral Density and Spectral Analysis
- 9. Linear Systems with Random Inputs
- 10. Gaussian Processes and Their Properties
- 11. Markov Chains and Counting Processes (Poisson Processes)
- 12. Estimation Theory: Least Squares and MMSE
- 13. Detection and Hypothesis Testing
- 14. Adaptive Filtering and Prediction
- 15. Applications to Communications, Radar, and Speech/Audio
Languages, Platforms & Tools
How It Compares
Covers similar foundational ground to Papoulis & Pillai's Probability, Random Variables, and Stochastic Processes but tends to be more accessible with engineering examples; compared with Peebles' Random Signal Principles, Stark emphasizes rigorous development of probabilistic tools before application.
