Haghighi A.M., Wickramasinghe I. Probability, Statistics, and Stochastic Processes for Engineers and Scientists

Boca Raton: CRC Press, 2020. — 635 p. — (Mathematical Engineering, Manufacturing, and Management Sciences). — ISBN: 0815375905, 9780815375906.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.FeaturesIncludes 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 queuesDedicationAuthors
Chapter PreliminariesSet and Its Basic Properties
Zermelo and Fraenkel (ZFC) Axiomatic Set Theory
Basic Concepts of Measure Theory
Lebesgue Integral
Counting
Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Measure
Exercises
Chapter Basics of Probability
Basics of Probability
Fuzzy Probability
Conditional Probability
Independence
The Law of Total Probability and Bayes’ Theorem
Exercises
Chapter Random Variables and Probability Distribution FunctionsDiscrete Probability Distribution (Mass) Functions (pmf)
Moments of a Discrete Random Variable
Arithmetic Average
Moments of a Discrete Random Variable
Basic Standard Discrete Probability Mass Functions
Discrete Uniform pmf
Bernoulli pmf
Binomial pmf
Geometric pmf
Negative Binomial pmf
Hypergeometric pmf
Poisson pmf
Probability Distribution Function (cdf) for a Continuous Random Variable
Moments of a Continuous Random Variable
Continuous Moment Generating Function
Functions of Random Variables
Some Popular Continuous Probability Distribution Functions
Continuous Uniform Distribution
Gamma Distribution
Exponential Distribution
Beta Distribution
Erlang Distribution
Normal Distribution
χ[sup()], Chi-Squared, Distribution
The F-Distribution
Student’s t-Distribution
Weibull Distribution
Lognormal Distribution
Logistic Distribution
Extreme Value Distribution
Asymptotic Probabilistic Convergence
Exercises
Chapter Descriptive Statistics
Introduction and History of Statistics
Basic Statistical Concepts
Data Collection
Sampling Techniques
Tabular and Graphical Techniques in Descriptive Statistics
Frequency Distribution for Qualitative Data
Bar Graph
Pie Chart
Frequency Distribution for Quantitative Data
Histogram
Stem-and-Leaf Plot
Dot Plot
Measures of Central Tendency
Measure of Relative Standing
Percentile
Quartile
z-Score
More Plots
Box-and-Whisker Plot
Scatter Plot
Measures of Variability
Range
Variance
Standard Deviation
Understanding the Standard Deviation
The Empirical Rule
Chebyshev’s Rule
Exercises
Chapter Inferential StatisticsEstimation and Hypothesis Testing
Point Estimation
Interval Estimation
Hypothesis Testing
Comparison of Means and Analysis of Variance (ANOVA)
Inference about Two Independent Population Means
Confidence Intervals for the Difference in Population Means
Hypothesis Test for the Difference in Population Means
Confidence Interval for the Difference in Means of Two Populations with Paired Data
Analysis of Variance (ANOVA)
ANOVA Implementation Steps
One-Way ANOVA
Exercises
Chapter Nonparametric Statistics
Why Nonparametric Statistics?
Chi-Square Tests
Goodness-of-Fit
Test of Independence
Test of Homogeneity
Single-Sample Nonparametric Statistic
Single-Sample Sign Test
Two-Sample Inference
Independent Two-Sample Inference Using Mann–Whitney Test
Dependent Two-Sample Inference Using Wilcoxon Signed-Rank Test
Inference Using More Than Two Samples
Independent Sample Inference Using the Kruskal–Wallis Test
Exercises
Chapter Stochastic ProcessesRandom Walk
Point Process
Classification of States of a Markov Chain/Process
Martingales
Queueing Processes
The Simplest Queueing Model, M/M/
An M/M/ Queueing System with Delayed Feedback
Number of Busy Periods
A MAP Single-Server Service Queueing System
Analysis of the Model
Service Station
Number of Tasks in the Service Station
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
An Illustrative Example
Multi-Server Queueing Model, M/M/c
A Stationary Multi-Server Queueing System with Balking and Reneging
Case s= (No Reneging)
Case s= (No Reneging)
Birth-and-Death Processes
Finite Pure Birth
B-D Process
Finite Birth-and-Death Process
Analysis
Busy Period
Fuzzy Queues/Quasi-B-D
Quasi-B-D
A Fuzzy Queueing Model as a QBD
Crisp Model
The Model in Fuzzy Environment
Performance Measures of Interest
Exercises
Appendix