Gatti P. Probability theory and mathematical statistics for engineers

Londonand New York. Spon Press. 2005. — 369 p.Probability Theory and Statistical Methods for Engineers describes 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.Probability theory
The concept of probability
Different approaches to the idea of probability
The classical definition
The relative frequency approach to probability
The subjective viewpointProbability: the axiomatic approachProbability spaces
Random variables and distribution functions
Characteristic and moment-generating functions
Miscellaneous complements
Summary and commentsThe multivariate case: random vectorsRandom vectors and their distribution functions
Moments and characteristic functions of random vectors
More on conditioned random variables
Functions of random vectors
Summary and commentsConvergences, limit theorems and the law of large numbersWeak convergence
Other types of convergence
The weak law of large numbers (WLLN)
The strong law of large numbers (SLLN)
The central limit theorem
Summary and commentsMathematical statistics
Statistics: preliminary ideas and basic notionsThe statistical model and some notes on sampling
Sample characteristics
Point estimation
Maximum likelihood estimates and some remarks on other estimation methods
Interval estimation
A few notes on other types of statistical intervals
Summary and commentsThe test of statistical hypothesesGeneral principles of hypotheses testing
Parametric hypotheses
Testing the type of distribution (goodness-of-fit tests)
Miscellaneous complements
Summary and commentsRegression, correlation and the method of least squaresThe general linear regression problem
Normal regression
Final remarks on regression
Summary and commentsAppendix A: elements of set theory
Basic definitions and properties
Functions and sets, equivalent sets and cardinality
Systems of sets: algebras and alfa-algebrasAppendix B: the Lebesgue integral – an overview
Introductory remarks
Measure spaces and the Lebesgue measure on the real line
Measurable functions and their properties
The abstract Lebesgue integral
Further results in integration and measure theory and their relation to probabilityThe Gamma Function Г(x)
Gamma distribution
The Xi² distribution
Student’s distribution
Fisher’s distribution
Some other probability distributions
A few final results