Probability and random processes : an introduction for applied scientists and engineers (Japan : McGraw-Hill, 1970)
Preface, This book, intended as a text for a first course in probability and random processes, can be used either for self-study or in a formal classroom setting.In the classroom context, the first eight chapters could form a one-semester subject on probability with the last six chapters (plus posible supplementary material at the discretion of the instructor) following as a semester course on random processes. Alternatively, most of the key ideas in both probability and random processes could be covered in one semester by a judicious selection of sections. The prerequisites are calculus for the first eight chapters and calculus plus a prior, or coneurrent, introduction to Fourier theory for the remainder. Over the past ten years or so I have taught this material to such disparate groups as first-year graduate students in electrical engineering and engineers and applied scientists trained in a variety of technical fields who have returned to the academic world for study some ten to twenty years after graduating from college. As that teaching progressed, I became increasingly convinced of the need for a text which, while directed towards students mainly interested in applications, would present to the student the underlying mathematical issues in a readable and technically honest way. In particular, I felt the need fora text which would give an indication as to how the theoretieal complexity of the more advanced mathematical treatments arises from the logical difficulties inherent in the subject and is not due simply to the natural (or unnatural) perversity of the mathematician. I hope that this is such a text. Since I believe strongly that each of un Jonrns by doing rather than by passive observation, I have atlempled to got he render to develop a significant fraction of the key concepts and results by including them in the exercises. The excersices in this book are thus an integral part of the text and should all be worked out by the render (except possibly the ones designated as supplementary), With his fact in mind, and since one of my main objectives was to write a text which could be used for self study, complete solutions to all of the excersices are available in a supplementary book by Professor Amedeo Odoni and myself. In view of the wide availability of other books in the field, however, it did not seem necessasry to also include a set of problemn without solutions for class quizzes and home problems. Since the spring of 1908 a project has been underway at the MIT Center for Advanced Engineering Study to develop a course on this material for use in industrial location, That course in based in part upon this book and in part upon net of videotape lectures made by Professor Harry L. Van 'Troen, Jr. F'urther information about the lectura tapes and an accompanying study guide may be obtained from the Director of the MI'T Center for Advanced Engineering Study, of the many poople who contributed to thin book n few get my special thanks: my students; th0 Bocretarien of the MIT Center for Advanced Engineering Study (in particular, Mrs., Elizabeth Liljegren Borken) for the typing of the various verwions of the manuscript; Richard H. Lee of WGBH, Boston, for critically reviewing most of the early chapters; John T. Fiteh of the MIT-CAES for critically reviewing the entire manuseript; Professor Harry L. Van Trees, Jr., for his comments and suggestions for changes; Professor Amedeo Odoni for working up the final version of the solutions to the exercises; and last, but not least, Professor Harold S. Mickley, Director of the MIT-CAES, for both his critical comments and his generous Bupport of the project. Wilbur B. Davenport, Jr.
1. Introduction. 1 Randomness and averages. -- 2 Empirical averages. -- 3 Relative frequency. -- 4 Stability. -- 5 Probability and statistical averages. - 6 Summary and preview. - References. -- 2. Sample points and sample spaces. 1 Introduction. -- 2 Events. -- 3 Algebra of events. -- 4 Partilions. -- 5 Sequences of events. - 6 Summary of definitons and formulas. -- References. -- 3. Probability. 1 Probabilily axioms. -- 2 Elementary properties of probability. -- 3 Probability spaces. - 4 The continuity theorem of probability. -- 5 Joint probability. -- 6 Conditional probability. - 7 Independent events. -- 8 Independent experiments. - 9 Summary of axioms, definitions, and formulas. -- References. -- 4. Random variables. -- 5. Random vectors. 1 Random variables. -- 2 Probability distributions, densities, and distribution functions. -- 3 Properties of probability distribution functions. -- 4 Derivations. -- 5 Probability densities. -- 6 Mixed random variables. -- 7 Summary of definitions and formulas. - References. -- 6. Functions of random variables. 1 Introduction. -- 2 Functions of random variables. -- 3 Functions of random vectors. - 4 One-to-one transformations. -- 5 Summary. - References. -- 7. Statistical averages. 1 Discrete random variables. -- 2 Eristence (discrete case). -- 3 Functions of discrete random variables. -- 4 Functions of discrele random vectors. -- 5 Extension to the continuous case. -- 6 Continuous-case examples and exercises. -- 7 Existence (continuous case). -- 8 Moments. -- 9 Joint moments. -- 10 Gaussian random vectors. -- 11 Conditional averages. - 12 Inequalities. -- 13 Summary of definitions and formulas. - References. -- 8. Estimation, sampling, and prediction. 1 Introduction. -- 2 The sample mean. - 3 Relative frequency. -- 4 Relative frequency (continued). - 5 Minimum-variance estimators. - 6 Prediction. -- 7 Linear prediction. -- 8 Summary of definitions and formulas. - References. -- 9. Random processes. 1 Bernoulli process. -- 2 Binomial process. -- 3 Sine wave process. - 4 Random process descriptions. -- 5 Stationarity. -- 6 Covariance and correlation functions. -- 7 Stationarily (continued). -- 8 Sampling a random process. -- 9 Periodic sampling. -- 10 Summary of definitions and formulas. - References. -- 10. Linear transformations. 1 Two-dimensional vectors. -- 2 N-dimensional vectors. -- 3 Matrix formulation. - 4 Time averages. - 5 Weighting functions. - 6 Output moments. -- 7 Summary of definitions and formulas. -- References. -- 11. Spectral analysis. 1 Introduction. -- 2 Sine wave in, sine wave out. -- 3 Fourier analysis. -- 4 Spectral density. -- 5 Some general properties of the spectral density. -- 6 Spectral analysis of linear Systems. -- 7 Narrowband filtering. -- 8 Cross-Spectral densities. -- 9 Epilogue. -- 10 Summary of definitions and formulas. - References. -- 12. Sums of independent random variables. 1 Introduction. -- 2 Independent increment processes. -- 3 Linear-functional equation. - 4 Characteristic function. - 5 Further properties of the characteristic function. -- 6 Joint-characteristic functions. -- 7 Independent increment processes (continued). -- 8 Probability generating functions. -- 9 Central limit theorem. -- 10 Summary of definitions and formulas. -- References. -- 13. The poisson process. 1 Introduction. -- 2 Poisson counting process. -- 3 Arrival times. -- 4 Interarrival times. -- 5 Renewal counting process. -- 6 Unordered arrival times. -- 7 Filtered poisson processes. -- 8 Random partitioning. -- 9 Summary of definitions and formula. - References. -- 14. Tha gaussian process. 1 Introduction. -- 2 Gaussian Random Vectors. -- 3 Gaussian Random Processes. -- 4 Narrowband Waveforms. -- 5 Narrowband Random Processes. -- 6 Narrowband Gaussian Processes. -- 7 Summary Of Definitions And Formulas. - References. - Bibliography. - Index.
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