Probability Theory and Mathematical Statistics for Engineers

Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables. The book underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vectors and their distributions, including conditional distributions of projections of a random vector, conditional numerical characteristics, and information contained in random variables. The book elaborates on the functions of random variables and estimation of parameters of distributions. Topics include frequency as a probability estimate, estimation of statistical characteristics, estimation of the expectation and covariance matrix of a random vector, and testing the hypotheses on the parameters of distributions. The text then takes a look at estimator theory and estimation of distributions. The book is a vital source of data for students, engineers, postgraduates of applied mathematics, and other institutes of higher technical education. Content: Other Titles of Interest, Page ii Front Matter, Page iii Copyright, Page iv PREFACE, Pages v-ix CHAPTER 1 - PROBABILITIES OF EVENTS, Pages 1-40 CHAPTER 2 - RANDOM VARIABLES, Pages 41-73 CHAPTER 3 - NUMERICAL CHARACTERISTICS OF RANDOM VARIABLES, Pages 74-113 CHAPTER 4 - PROJECTIONS OF RANDOM VECTORS AND THEIR DISTRIBUTIONS, Pages 114-156 CHAPTER 5 - FUNCTIONS OF RANDOM VARIABLES, Pages 157-199 CHAPTER 6 - ESTIMATION OF PARAMETERS OF DISTRIBUTIONS, Pages 200-241 CHAPTER 7 - ESTIMATOR THEORY, Pages 242-272 CHAPTER 8 - ESTIMATION OF DISTRIBUTIONS, Pages 273-310 CHAPTER 9 - STATISTICAL MODELS, I, Pages 311-358 CHAPTER 10 - STATISTICAL MODELS, II, Pages 359-416 APPENDICES, Pages 417-435 MAIN NOTATIONS, Pages 436-438 REFERENCES, Pages 439-444 INDEX, Pages 445-450