Applied Probability and Statistics

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Springer Science & Business Media, May 4, 2006 - Mathematics - 358 pages
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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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Contents

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
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