Probability Random Variables & Stochastic Processes (3rd Ed)

by PAPOULIS

• ISBN13: 9780070484771
• ISBN10: 0070484775
• Edition: 3rd
• Format: Hardcover
• Copyright: 1991-01-01
• Publisher: McGraw Hill College Div

Summary

The Third Edition emphasizes a concentrated revision of Parts II & III (leaving Part I virtually intact). The later sections show greater elaboration of the basic concepts of stochastic processes, typical sequences of random variables, and a greater emphasis on realistic methods of spectral estimation and analysis. There are problems, exercises, and applications throughout. Aimed at senior/graduate students in electrical engineering, math, and physics departments.

Table of Contents

Preface to the Third Edition	xi	(2)
Preface to the Second Edition	xiii	(2)
Preface to the First Edition	xv
Part I Probability and Random Variables	3	(282)
1 The Meaning of Probability	3	(12)
1-1 Introduction	3	(2)
1-2 The Definitions	5	(7)
1-3 Probability and Induction	12	(1)
1-4 Causality versus Randomness	13	(2)
2 The Axioms of Probability	15	(23)
2-1 Set Theory	15	(5)
2-2 Probability Space	20	(7)
2-3 Conditional Probability	27	(9)
Problems	36	(2)
3 Repeated Trials	38	(25)
3-1 Combined Experiments	38	(5)
3-2 Bernoulli Trials	43	(4)
3-3 Asymptotic Theorems	47	(8)
3-4 Poisson Theorem and Random Points	55	(5)
Problems	60	(3)
4 The Concept of a Random Variable	63	(23)
4-1 Introduction	63	(3)
4-2 Distribution and Density Functions	66	(7)
4-3 Special Cases	73	(6)
4-4 Conditional Distributions and Total Probability	79	(5)
Problems	84	(2)
5 Functions of One Random Variable	86	(38)
5-1 The Random Variable g(x)	86	(1)
5-2 The Distribution of g(x)	87	(15)
5-3 Mean and Variance	102	(7)
5-4 Moments	109	(6)
5-5 Characteristic Functions	115	(5)
Problems	120	(4)
6 Two Random Variables	124	(27)
6-1 Bivariate Distributions	124	(11)
6-2 One Function of Two Random Variables	135	(7)
6-3 Two Functions of Two Random Variables	142	(6)
Problems	148	(3)
7 Moments and Conditional Distributions	151	(31)
7-1 Joint Moments	151	(6)
7-2 Joint Characteristic Functions	157	(5)
7-3 Conditional Distributions	162	(7)
7-4 Conditional Expected Values	169	(4)
7-5 Mean Square Estimation	173	(6)
Problems	179	(3)
8 Sequences of Random Variables	182	(59)
8-1 General Concepts	182	(10)
8-2 Conditional Densities, Characteristic Functions, and Normality	192	(9)
8-3 Mean Square Estimation	201	(7)
8-4 Stochastic Convergence and Limit Theorems	208	(13)
8-5 Random Numbers: Meaning and Generation	221	(16)
Problems	237	(4)
9 Statistics	241	(44)
9-1 Introduction	241	(3)
9-2 Parameter Estimation	244	(21)
9-3 Hypothesis Testing	265	(14)
Problems	279	(6)
Part II Stochastic Processes	285	(373)
10 General Concepts	285	(60)
10-1 Definitions	285	(18)
10-2 Systems with Stochastic Inputs	303	(16)
10-3 The Power Spectrum	319	(13)
10-4 Digital Processes	332	(4)
Appendix 10A Continuity, Differentiation, Integration	336	(3)
Appendix 10B Shift Operators and Stationary Processes	339	(1)
Problems	340	(5)
11 Basic Applications	345	(56)
11-1 Random Walk, Brownian Motion, and Thermal Noise	345	(9)
11-2 Poisson Points and Shot Noise	354	(8)
11-3 Modulation	362	(11)
11-4 Cyclostationary Processes	373	(3)
11-5 Bandlimited Processes and Sampling Theory	376	(8)
11-6 Deterministic Signals in Noise	384	(5)
11-7 Bispectra and System Identification	389	(6)
Appendix 11A The Poisson Sum Formula	395	(1)
Appendix 11B Schwarz's Inequality	395	(1)
Problems	396	(5)
12 Spectral Representation	401	(26)
12-1 Factorization and Innovations	401	(3)
12-2 Finite-Order Systems and State Variables	404	(8)
12-3 Fourier Series and Karhunen-Loeve Expansions	412	(4)
12-4 Spectral Representation of Random Processes	416	(9)
Problems	425	(2)
13 Spectral Estimation	427	(53)
13-1 Ergodicity	427	(16)
13-2 Spectral Estimation	443	(12)
13-3 Extrapolation and System Identification	455	(19)
Appendix 13A Minimum-Phase Functions	474	(1)
Appendix 13B All-Pass Functions	475	(2)
Problems	477	(3)
14 Mean Square Estimation	480	(53)
14-1 Introduction	480	(7)
14-2 Prediction	487	(21)
14-3 Filtering and Prediction	508	(7)
14-4 Kalman Filters	515	(14)
Problems	529	(4)
15 Entropy	533	(70)
15-1 Introduction	533	(9)
15-2 Basic Concepts	542	(16)
15-3 Random Variables and Stochastic Processes	558	(11)
15-4 The Maximum Entropy Method	569	(10)
15-5 Coding	579	(12)
15-6 Channel Capacity	591	(9)
Problems	600	(3)
16 Selected Topics	603	(55)
16-1 The Level-Crossing Problem	603	(9)
16-2 Queueing Theory	612	(17)
16-3 Shot Noise	629	(6)
16-4 Markoff Processes	635	(19)
Problems	654	(4)
Bibliography	658	(3)
Index	661