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E-grāmata: Probability, Statistics, and Stochastic Processes for Engineers and Scientists [Taylor & Francis e-book]

(Prairie View A&M University, TX, USA), (Prairie View A&M University, Houston, Texas)
  • Formāts: 620 pages, 165 Tables, black and white; 94 Line drawings, black and white; 26 Halftones, black and white; 120 Illustrations, black and white
  • Sērija : Engineering Mathematics and Operations Research
  • Izdošanas datums: 01-Jul-2022
  • Izdevniecība: CRC Press
  • ISBN-13: 9781351238403
Citas grāmatas par šo tēmu:
  • Taylor & Francis e-book
  • Cena: 222,34 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Standarta cena: 317,63 €
  • Ietaupiet 30%
Probability, Statistics, and Stochastic Processes for Engineers and ScientistsPalielināt
  • Formāts: 620 pages, 165 Tables, black and white; 94 Line drawings, black and white; 26 Halftones, black and white; 120 Illustrations, black and white
  • Sērija : Engineering Mathematics and Operations Research
  • Izdošanas datums: 01-Jul-2022
  • Izdevniecība: CRC Press
  • ISBN-13: 9781351238403
Citas grāmatas par šo tēmu:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Rokasgrāmatas mājas lapa: https://www.taylorfrancis.com/books/9781351238403

Featuring recent advances in probability, statistics, and stochastic processes, this new textbook presents Probability and Statistics, and an introduction to Stochastic Processes.



2020 Taylor & Francis Award Winner for Outstanding New Textbook!

Featuring recent advances in the field, this new textbook presents probability and statistics, and their applications in stochastic processes. This 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 in this field that combines these areas in one book, balances both theory and practical applications, and also keeps 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 (continuous time such as waiting time, and fuzzy and discrete time like the classic Gambler’s Ruin Problem)

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

  • Different types of computer software such as MATLAB®, Minitab, MS Excel, and R as options for illustration, programing and calculation purposes and data analysis

    • 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 t-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, M/M/c
    		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 Takįcs; 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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