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E-raamat: Probability, Statistics, and Stochastic Processes for Engineers and Scientists

(Prairie View A&M University, TX, USA), , (Prairie View A&M University, Houston, Texas)
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"Featuring recent advances in probability, statistics, and stochastic processes, this new textbook presents Probability and Statistics, and an introduction to Stochastic Processes. The book presents key information for understanding the essential aspectsof basic probability theory and concepts of reliability as an application. The purpose of this book is to provide an option that combines these areas into one resource, balancing both theory, practical applications, and also keeping the practitioners in mind"--

Featuring recent advances in probability, statistics, and stochastic processes, this new textbook presents Probability and Statistics, and an introduction to Stochastic Processes. The book presents key information for understanding the essential aspects of basic probability theory and concepts of reliability as an application. The purpose of this book is to provide an option that combines these areas into one resource, balancing both theory, practical applications, and also keeping the practitioners in mind.

Features

  • Includes numerous examples using current technologies with applications in various fields of study

  • Offers many practical applications of probability in queueing models, all of which are related to the appropriate stochastic processes such as the classic Gambler's Ruin Problem

  • Discusses current topics such as probability distributions used in real-world applications of statistics such as climate control and pollution

  • Illustrates how to use different options for calculation purposes and data analysis such as, Minitab, MS Excel, and R Programming

  • Covers reliability and its application in network queues

Preface xi
Authors xiii
Chapter 1 Preliminaries
1(50)
1.1 Introduction
1(2)
1.2 Set and Its Basic Properties
3(11)
1.3 Zermelo and Fraenkel (ZFC) Axiomatic Set Theory
14(6)
1.4 Basic Concepts of Measure Theory
20(8)
1.5 Lebesgue Integral
28(4)
1.6 Counting
32(10)
1.7 Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Measure
42(9)
Exercises
48(3)
Chapter 2 Basics of Probability
51(36)
2.1 Basics of Probability
51(10)
2.2 Fuzzy Probability
61(1)
2.3 Conditional Probability
62(4)
2.4 Independence
66(4)
2.5 The Law of Total Probability and Bayes' Theorem
70(17)
Exercises
80(7)
Chapter 3 Random Variables and Probability Distribution Functions
87(210)
3.1 Introduction
87(6)
3.2 Discrete Probability Distribution (Mass) Functions (pmf)
93(3)
3.3 Moments of a Discrete Random Variable
96(27)
3.3.1 Arithmetic Average
96(3)
3.3.2 Moments of a Discrete Random Variable
99(24)
3.4 Basic Standard Discrete Probability Mass Functions
123(42)
3.4.1 Discrete Uniform pmf
123(2)
3.4.2 Bernoulli pmf
125(5)
3.4.3 Binomial pmf
130(10)
3.4.4 Geometric pmf
140(8)
3.4.5 Negative Binomial pmf
148(2)
3.4.6 Hypergeometric pmf
150(5)
3.4.7 Poisson pmf
155(10)
3.5 Probability Distribution Function (cdf) for a Continuous Random Variable
165(6)
3.6 Moments of a Continuous Random Variable
171(4)
3.7 Continuous Moment Generating Function
175(1)
3.8 Functions of Random Variables
176(11)
3.9 Some Popular Continuous Probability Distribution Functions
187(83)
3.9.1 Continuous Uniform Distribution
188(3)
3.9.2 Gamma Distribution
191(2)
3.9.3 Exponential Distribution
193(7)
3.9.4 Beta Distribution
200(9)
3.9.5 Erlang Distribution
209(5)
3.9.6 Normal Distribution
214(23)
3.9.7 Χ2, Chi-Squared, Distribution
237(2)
3.9.8 The F-Distribution
239(5)
3.9.9 Student's f-Distribution
244(8)
3.9.10 Weibull Distribution
252(5)
3.9.11 Lognormal Distribution
257(3)
3.9.12 Logistic Distribution
260(4)
3.9.13 Extreme Value Distribution
264(6)
3.10 Asymptotic Probabilistic Convergence
270(27)
Exercises
288(9)
Chapter 4 Descriptive Statistics
297(58)
4.1 Introduction and History of Statistics
297(1)
4.2 Basic Statistical Concepts
297(3)
4.2.1 Data Collection
298(2)
4.3 Sampling Techniques
300(1)
4.4 Tabular and Graphical Techniques in Descriptive Statistics
301(18)
4.4.1 Frequency Distribution for Qualitative Data
301(1)
4.4.2 Bar Graph
302(2)
4.4.3 Pie Chart
304(2)
4.4.4 Frequency Distribution for Quantitative Data
306(3)
4.4.5 Histogram
309(8)
4.4.6 Stem-and-Leaf Plot
317(1)
4.4.7 Dot Plot
318(1)
4.5 Measures of Central Tendency
319(8)
4.6 Measure of Relative Standing
327(10)
4.6.1 Percentile
327(2)
4.6.2 Quartile
329(7)
4.6.3 z-Score
336(1)
4.7 More Plots
337(4)
4.7.1 Box-and-Whisker Plot
337(3)
4.7.2 Scatter Plot
340(1)
4.8 Measures of Variability
341(6)
4.8.1 Range
342(1)
4.8.2 Variance
342(3)
4.8.3 Standard Deviation
345(2)
4.9 Understanding the Standard Deviation
347(8)
4.9.1 The Empirical Rule
347(1)
4.9.2 Chebyshev's Rule
348(1)
Exercises
349(6)
Chapter 5 Inferential Statistics
355(72)
5.1 Introduction
355(2)
5.2 Estimation and Hypothesis Testing
357(50)
5.2.1 Point Estimation
358(27)
5.2.2 Interval Estimation
385(8)
5.2.3 Hypothesis Testing
393(14)
5.3 Comparison of Means and Analysis of Variance (ANOVA)
407(20)
5.3.1 Inference about Two Independent Population Means
408(1)
5.3.1.1 Confidence Intervals for the Difference in Population Means
408(1)
5.3.1.2 Hypothesis Test for the Difference in Population Means
409(5)
5.3.2 Confidence Interval for the Difference in Means of Two Populations with Paired Data
414(1)
5.3.3 Analysis of Variance (ANOVA)
415(1)
5.3.3.1 ANOVA Implementation Steps
416(1)
5.3.3.2 One-Way ANOVA
417(8)
Exercises
425(2)
Chapter 6 Nonparametric Statistics
427(36)
6.1 Why Nonparametric Statistics?
427(1)
6.2 Chi-Square Tests
428(8)
6.2.1 Goodness-of-Fit
428(3)
6.2.2 Test of Independence
431(3)
6.2.3 Test of Homogeneity
434(2)
6.3 Single-Sample Nonparametric Statistic
436(4)
6.3.1 Single-Sample Sign Test
436(4)
6.3 Two-Sample Inference
440(12)
6.3.1 Independent Two-Sample Inference Using Mann-Whitney Test
441(8)
6.3.2 Dependent Two-Sample Inference Using Wilcoxon Signed-Rank Test
449(3)
6.4 Inference Using More Than Two Samples
452(11)
6.4.1 Independent Sample Inference Using the Kruskal-Wallis Test
452(5)
Exercises
457(6)
Chapter 7 Stochastic Processes
463(118)
7.1 Introduction
463(2)
7.2 Random Walk
465(7)
7.3 Point Process
472(17)
7.4 Classification of States of a Markov Chain/Process
489(3)
7.5 Martingales
492(5)
7.6 Queueing Processes
497(51)
7.6.1 The Simplest Queueing Model, M/M/1
497(10)
7.6.2 An M/M/1 Queueing System with Delayed Feedback
507(8)
7.6.2.1 Number of Busy Periods
515(4)
7.6.3 A MAP Single-Server Service Queueing System
519(1)
7.6.3.1 Analysis of the Model
520(2)
7.6.3.2 Service Station
522(1)
7.6.3.3 Number of Tasks in the Service Station
523(1)
7.6.3.4 Stepwise Explicit Joint Distribution of the Number of Tasks in the System: General Case When Batch Sizes Vary between a Minimum k and a Maximum K
524(2)
7.6.3.5 An Illustrative Example
526(15)
7.6.4 Multi-Server Queueing Model, MIMIc
541(1)
7.6.4.1 A Stationary Multi-Server Queueing System with Balking and Reneging
541(3)
7.6.4.2 Case s = 0 (No Reneging)
544(2)
7.6.4.3 Case s = 0 (No Reneging)
546(2)
7.7 Birth-and-Death Processes
548(20)
7.7.1 Finite Pure Birth
550(2)
7.7.2 B-D Process
552(6)
7.7.3 Finite Birth-and-Death Process
558(1)
7.7.3.1 Analysis
558(3)
7.7.3.2 Busy Period
561(7)
7.8 Fuzzy Queues/Quasi-B-D
568(13)
7.8.1 Quasi-B-D
568(1)
7.8.2 A Fuzzy Queueing Model as a QBD
569(1)
7.8.2.1 Crisp Model
569(1)
7.8.2.2 The Model in Fuzzy Environment
570(3)
7.8.2.3 Performance Measures of Interest
573(5)
Exercises
578(3)
Appendix 581(16)
Bibliography 597(12)
Index 609
Dr. Aliakbar Montazer Haghighi is Professor and Head of the Mathematics Department at Prairie View A&M University, Texas, USA. He received his Ph. D. in Probability and Statistics from Case Western Reserve University, Cleveland, Ohio, USA, under supervision of Lajos Takács; and his BA and MA in Mathematics from San Francisco State University, California. He has years of teaching, research and academic and administrative experiences at various universities globally. His research publications are extensive; they include mathematics books and Lecture Notes written in English and Farsi. His latest book with D.P. Mishev as co-author, titled "Delayed and Network Queues" appeared in September of 2016 was published by John Wiley & Sons Inc., New Jersey, USA; and his last Book-Chapter with D.P. Mishev as co-author, Stochastic Modeling in Indusry and Management, Chapter 7 of "A Modeling and Simulation in Industrial Engineering", Mangey Ram and J. P. Davim, Editors, to appear in 2018 by Springer. He is a life-time member of AMS and SIAM. He is the Co-Founder and is the Editor-in-Chief of Application and Applied Mathematics: An International Journal (AAM), http://www.pvamu.edu/aam. More about him may be viewed at https://www.pvamu.edu/bcas/departments/mathematics/faculty-and-staff/amhaghig hi/.



Dr. Indika Rathnathungalage Wickramasinghe is an Assistant Professor in the Department of Mathematics at Prairie View A&M University, Texas, USA. He received his Ph. D. in Mathematical Statistics from Texas Tech University, Lubbock, Texas, USA, under supervision of Dr. Alex Trindade; MS in Statistics from Texas Tech University, Lubbock, Texas, USA; MSc in Operations Research from Moratuwa University, Sri Lanka and BSc in Mathematics from University of Kelaniya, Sri Lanka. He has over 15 years of teaching and research experiences at various universities globally. Dr. Wickramasinghe has individually and collaboratively published a number of research publications and successfully submitted several grant proposals. More information about him may be viewed at https://www.pvamu.edu/bcas/departments/mathematics/faculty-and- staff/iprathnathungalage/
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