Customer Reviews

Probability and Stochastic Processes for Engineers

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Written by one of the founding fathers in this area, the book is filled with illuminating practical examples and (more importantly) ways to think about these types of problems. I used it in grad school and I still use it today in practice. A classic.

This text is for me the best text in the probability/stochastic processes area for engineers and phycisists alike.The explanations are cristal clear,the subject coverage complete and the text organization impeccable.A lot of very instructive examples from communication theory,physics and electrical engineering.I think this book is a must expecially if you want to specialize in communications.Greatly outperforms Papoulis book on the same subject.5 stars!

I am using this book in my professional research, long after college, so I can be objective, now that the pain inflicted by the author is gone.

Fellow reviewer Luca Rinaldi said it best: the organization of this book is impeccable.

That, IMHO, is what makes this still the best probability book in print.

I had the misfortune of using both this book and the second edition of Stark & Woods in college. I think my professors chose the Stark & Woods book because it came with BASIC/MATLAB code on a 3.5" floppy disk, whereas Helstrom did not come with code, and they figured they'd be doing the students a favor by introducing them to tangible MATLAB code. If so, I think that that was a mistake. Engineers who study probability, especially electrical engineers, are usually capable of writing their own code without help from a probability book. And for a time-limited course, the code will not be so extensive anyway, so it's not like a code addendum will be a huge time saver. It takes no more than 5 minutes to code up a Guassian PDF in BASIC.

Next, compare the structure of Helstrom:

Chapter 1: Probability
Chapter 2: Random Variables
Chapter 3: Bivariate Probability Distributions
Chapter 4: Multiple Random Variables
Chapter 5: Discrete-Time Stochastic Processes
Chapter 6: Continous-Time Stochastic Processes
Chapter 7: Estimation and Detection
Appendix A: The Error-Function Integral

...to the structure of Stark & Woods:

Chapter 1: Introduction to Probability
Chapter 2: Random Variables
Chapter 3: Functions of Random Variables
Chapter 4: Averages
Chapter 5: Vector Random Variables
Chapter 6: Estimation and Decision Theory I
Chapter 7: Random Sequences
Chapter 8: Random Processes
Chapter 9: Mean-Square Calculus
Chapter 10: Stationary Proesses and Sequences
Chapter 11: Estimation Theory II
Appendix: Review of Relevant Mathematics

We can see from Helstrom that the organization of the body of knowledge of probability and stochastic processes has an inherent, fundamental structure, and this organization is readily ascertained from his table of contents, as Helstrom notes in his Preface.

Stark & Woods, on the other hand, chose to introduce random variables in Chapter 2, including the Gaussian and Poisson distributions, then waiting until Chapter 4 to explain what the mean and variance are in distributions. They include a brief, necessarily non-rigorous, introduction to the Dirac delta function in Chapter 2. And then there is the computation of conditional and joint distributions in Chapter 2, conversion of Guassian to Standard Normal, and a passing mention of Bose-Einstein statistics, all in Chapter 2, before there is an explanation of what is "mu" in a PDF, which does not come until Chapter 4.

Both Helstrom and Stark & Woods "sprinkle" various applications of probabilty throughout their respective texts, but what makes Helstrom better, again, is the organization. Helstrom's applications are never introduced before the reader has had the opportunity to gain full context, presuming that the reader has read the chapters in order. Helstrom is meticulous about this policy: he is acutely aware of what has been said and what not so far in his book. This a kind of discipline/restraint in Helstrom that is not as present in Stark & Woods. For example, Helstrom notes in his Preface that "Acquaintance with the Laplace inversion integral and the residue theorem will be helpful in Chapter 7." Stark & Woods defines an entire section 10.APP, "Residue Method For Inverse Fourier Transformation" at the end of Chapter 10, even though there is an "Appendix: Review of Relevant Mathmatics". By deferring to the student's prior exposure to the residue theorem, Helstrom is implicitly stating that it is best for an author to remain within the realm of the subject matter and resist the urge to deviate, because the subject of probability itself is already vast, and it is impossible to include everything. If necessary, the student can read elsewhere about the residue theorem. Many authors struggle with this question of scope. I think that Helstrom got it right: restraint is the best policy.

The only thing I regret about Helstrom is that he, the person, is very hard to track down!!!