Probability Theory and Mathematical Statistics for Engineers

by Gatti; Paolo L.

• ISBN13: 9780415251723
• ISBN10: 0415251729
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-12-16
• Publisher: CRC Press

Summary

Probability Theory and Statistical Methods for Engineersdescribes the fundamental concepts and applications of probability and statistics. By bringing together modern probability theory with the more practical applications of statistics, it bridges the gap between theory and practice. Topics such as, for example, Fourier transforms and stochastic processes are presented as a series of methods or recipes which can be applied to specific problems, but for this they need to be well understood. This book is essential reading for practicing engineers who need a sound background knowledge of probabilistic and statistical concepts and methods of analysis for their everyday work. It is also a useful guide for graduate engineering students.

Author Biography

Paolo L. Gatti was formerly Head of the Vibration Testing and Data Acquisition Division of Tecniter s.r.l., Cassina de' Pecchi, Milan, Italy.

Table of Contents

Preface	x
PART I Probability theory	1	(160)
1 The concept of probability	3	(19)
1.1 Different approaches to the idea of probability	3	(1)
1.2 The classical definition	4	(10)
1.3 The relative frequency approach to probability	14	(4)
1.4 The subjective viewpoint	18	(1)
1.5 Summary	19	(3)
2 Probability: the axiomatic approach	22	(54)
2.1 Introduction	22	(1)
2.2 Probability spaces	22	(11)
2.3 Random variables and distribution functions	33	(22)
2.4 Characteristic and moment-generating functions	55	(8)
2.5 Miscellaneous complements	63	(9)
2.6 Summary and comments	72	(4)
3 The multivariate case: random vectors	76	(53)
3.1 Introduction	76	(1)
3.2 Random vectors and their distribution functions	76	(9)
3.3 Moments and characteristic functions of random vectors	85	(18)
3.4 More on conditioned random variables	103	(12)
3.5 Functions of random vectors	115	(11)
3.6 Summary and comments	126	(3)
4 Convergences, limit theorems and the law of large numbers	129	(32)
4.1 Introduction	129	(1)
4.2 Weak convergence	130	(7)
4.3 Other types of convergence	137	(5)
4.4 The weak law of large numbers (WLLN)	142	(4)
4.5 The strong law of large numbers (SLLN)	146	(3)
4.6 The central limit theorem	149	(8)
4.7 Summary and comments	157	(4)
PART II Mathematical statistics	161	(145)
5 Statistics: preliminary ideas and basic notions	163	(60)
5.1 Introduction	163	(1)
5.2 The statistical model and some notes on sampling	164	(4)
5.3 Sample characteristics	168	(12)
5.4 Point estimation	180	(16)
5.5 Maximum likelihood estimates and some remarks on other estimation methods	196	(8)
5.6 Interval estimation	204	(13)
5.7 A few notes on other types of statistical intervals	217	(1)
5.8 Summary and comments	218	(5)
6 The test of statistical hypotheses	223	(51)
6.1 Introduction	223	(1)
6.2 General principles of hypotheses testing	223	(3)
6.3 Parametric hypotheses	226	(25)
6.4 Testing the type of distribution (goodness-of-fit tests)	251	(11)
6.5 Miscellaneous complements	262	(9)
6.6 Summary and comments	271	(3)
7 Regression, correlation and the method of least squares	274	(32)
7.1 Introduction	274	(1)
7.2 The general linear regression problem	275	(10)
7.3 Normal regression	285	(13)
7.4 Final remarks on regression	298	(5)
7.5 Summary and comments	303	(3)
Appendix A: elements of set theory	306	(12)
A.1 Basic definitions and properties	306	(6)
A.2 Functions and sets, equivalent sets and cardinality	312	(3)
A.3 Systems of sets: algebras and σ-algebras	315	(3)
Appendix B: the Lebesgue integral - an overview	318	(19)
B.1 Introductory remarks	318	(1)
B.2 Measure spaces and the Lebesgue measure on the real line	319	(2)
B.3 Measurable functions and their properties	321	(3)
B.4 The abstract Lebesgue integral	324	(6)
B.5 Further results in integration and measure theory and their relation to probability	330	(7)
Appendix C	337	(16)
C.1 The Gamma Function Γ(x)	337	(1)
C.2 Gamma distribution	338	(1)
C.3 The χ² distribution	339	(1)
C.4 Student's distribution	340	(2)
C.5 Fisher's distribution	342	(2)
C.6 Some other probability distributions	344	(6)
C.7 A few final results	350	(3)
Index	353