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.

Table of Contents

1 Introduction to Probability

2 Random Variables

3 Functions of Random Variables

4 Expectation and Moments

5 Random Vectors

6 Statistics: Part 1 Parameter Estimation

7 Statistics: Part 2 Hypothesis Testing

8 Random Sequences

9 Random Processes

10 Advanced Topics in Random Processes

11 Applications to Statistical Signal Processing

Appendix A: Review of Relevant Mathematics

Appendix B: Gamma and Delta Functions

Appendix C: Functional Transformations and Jacobians

Appendix D: Measure and Probability

Appendix E: Sampled Analog Waveforms and Discrete-time Signals

Appendix F: Independence of Sample Mean and Variance for Normal Random Variables

Appendix G: Tables of Cumulative Distribution Functions: the Normal, Student t, Chi-square, and F