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Basic Probability Theory with Applications : Springer Undergraduate Texts in Mathematics and Technology - Mario Lefebvre

Basic Probability Theory with Applications

Springer Undergraduate Texts in Mathematics and Technology


Published: August 2009
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This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the all important central limit theorem, are treated next. The last three chapters concentrate on applications of this theory in the areas of reliability theory, basic queuing models, and time series. Examples are elegantly woven into the text and over 400 exercises reinforce the material and provide students with ample practice.

This textbook can be used by undergraduate students in pure and applied sciences such as mathematics, engineering, computer science, finance and economics.

A separate solutions manual is available to instructors who adopt the text for their course.

From the reviews: "This book's introductory sections on probability theory are typical of most textbooks in the content of presentation ... . There are many examples with detailed solutions and a large number of exercises are included at the ends of the chapters. ... used as a textbook for engineers, computer scientists and ... students in economics and finance will be able to understand it. This book would be my choice for a textbook if I were to teach a course in probability theory for math majors." (Charles Ashbacher, The Mathematical Association of America, November, 2009) "This textbook is designed for a course in probability theory at the undergraduate post-calculus level. ... The book should be a good choice for a course at the indicated level." (Gerald A. Heuer, Zentralblatt MATH, Vol. 1192, 2010)

Prefacep. vi
List of Tablesp. xiii
List of Figuresp. xv
Review of differential calculusp. 1
Limits and continuityp. 1
Derivativesp. 3
Integralsp. 7
Particular integration techniquesp. 9
Double integralsp. 12
Infinite seriesp. 14
Geometric seriesp. 15
Exercises for Chapter 1p. 18
Elementary probabilityp. 27
Random experimentsp. 27
Eventsp. 28
Probabilityp. 29
Conditional probabilityp. 32
Total probabilityp. 35
Combinatorial analysisp. 36
Exercises for Chapter 2p. 39
Random variablesp. 55
Introductionp. 55
Discrete casep. 55
Continuous casep. 57
Important discrete random variablesp. 61
Binomial distributionp. 61
Geometric and negative binomial distributionsp. 64
Hypergeometric distributionp. 66
Poisson distribution and processp. 68
Important continuous random variablesp. 70
Normal distributionp. 70
Gamma distributionp. 74
Weibull distributionp. 77
Beta distributionp. 78
Lognormal distributionp. 80
Functions of Random variablesp. 81
Discrete casep. 81
Continuous casep. 82
Characteristics of random variablesp. 83
Exercises for Chapter 3p. 94
Random vectorsp. 115
Discrete random vectorsp. 115
Continuous random vectorsp. 118
Functions of random vectorsp. 124
Discrete casep. 125
Continuous casep. 127
Convolutionsp. 128
Covariance and correlation coefficientp. 131
Limit theoremsp. 135
Exercises for Chapter 4p. 137
Reliabilityp. 161
Basic notionsp. 161
Reliability of systemsp. 170
Systems in seriesp. 170
Systems in parallelp. 172
Other casesp. 176
Paths and cutsp. 178
Exercises for Chapter 5p. 183
Queueingp. 191
Continuous-time Markov chainsp. 191
Quening systems with a single serverp. 197
The M/M/1 modelp. 199
The M/M/1 model with finite capacityp. 207
Queueing systems with two or more serversp. 212
The M/M/s modelp. 212
The M/M/s/c modelp. 218
Exercises for Chapter 6p. 220
Time seriesp. 227
Introductionp. 227
Particular time series modelsp. 235
Autoregressive processesp. 235
Moving average processesp. 244
Autoregressive moving average processesp. 249
Modeling and forecastingp. 251
Exercises for Chapter 7p. 261
List of symbols and abbreviationsp. 269
Statistical tablesp. 275
Solutions to "Solved exercises"p. 281
Answers to even-numbered exercisesp. 325
Answers to multiple choice questionsp. 333
Referencesp. 335
Indexp. 337
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780387749945
ISBN-10: 0387749942
Series: Springer Undergraduate Texts in Mathematics and Technology
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 340
Published: August 2009
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 17.8  x 2.29
Weight (kg): 0.81