Applied Probability and Statistics

Springer Science & Business Media, 04.05.2006 - 358 Seiten
This book is based mainly on the lecture notes that I have been using since 1993 for a course on applied probability for engineers that I teach at the Ecole Polytechnique de Montreal. This course is given to electrical, computer and physics engineering students, and is normally taken during the second or third year of their curriculum. Therefore, we assume that the reader has acquired a basic knowledge of differential and integral calculus. The main objective of this textbook is to provide a reference that covers the topics that every student in pure or applied sciences, such as physics, computer science, engineering, etc., should learn in probability theory, in addition to the basic notions of stochastic processes and statistics. It is not easy to find a single work on all these topics that is both succinct and also accessible to non-mathematicians. Because the students, who for the most part have never taken a course on prob ability theory, must do a lot of exercises in order to master the material presented, I included a very large number of problems in the book, some of which are solved in detail. Most of the exercises proposed after each chapter are problems written es pecially for examinations over the years. They are not, in general, routine problems, like the ones found in numerous textbooks.

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Inhalt

 Introduction1 2 12 Examples of Applications 3 13 Relative Frequencies 5 Elementary Probabilities 7 22 Probability 10 23 Combinatorial Analysis 13 24 Conditional Probability 18 25 Independence 21
 412 Exercises Problems and Multiple Choice Questions 195 Stochastic Processes 220 52 Characteristics of Stochastic Processes 222 53 Markov Chains 225 54 The Poisson Process 228 55 The Wiener Process 232 56 Stationarity 235 57 Ergodicity 238

 26 Exercises Problems and Multiple Choice Questions Solved Exercises 26 Random Variables 55 32 The Distribution Function 57 33 The Probability Mass and Density Functions 64 34 Important Discrete Random Variables 70 35 Important Continuous Random Variables 82 36 Transformations 92 37 Mathematical Expectation and Variance 95 38 Transforms 103 39 Reliability 108 310 Exercises Problems and Multiple Choice Questions Solved Exercises 111 Random Vectors 157 42 Random Vectors of Dimension 2 158 43 Conditionals 166 44 Random Vectors of Dimension n 2 170 45 Transformations of Random Vectors 172 46 Covariance and Correlation 176 47 Multinormal Distribution 179 48 Estimation of a Random Variable 182 49 Linear Combinations 185 410 The Laws of Large Numbers 188 411 The Central Limit Theorem 189
 58 Exercises Problems and Multiple Choice Questions Solved Exercises 240 Estimation and Testing 253 62 Estimation by Confidence Intervals 258 63 Pearsons ChiSquare GoodnessofFit Test 262 64 Tests of Hypotheses on the Parameters 266 65 Exercises Problems and Multiple Choice Questions Supplementary Exercises 279 Simple Linear Regression 307 72 Tests of Hypotheses 310 73 Confidence Intervals and Ellipses 313 74 The Coefficient of Determination 315 76 Curvilinear Regression 318 77 Correlation 321 78 Exercises Problems and Multiple Choice Questions Supplementary Exercises 324 Mathematical Formulas 339 Quantiles of the Sampling Distributions 341 Classification of the Exercises 344 Answers to the Multiple Choice Questions 347 Answers to Selected Supplementary Exercises 349 Bibliography 351 Index 353 Urheberrecht