Probability, Statistics, and Stochastic Processes for Engineers and Scientists ()

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Authors
Chapter 1 Preliminaries
	1.1 Introduction
	1.2 Set and Its Basic Properties
	1.3 Zermelo and Fraenkel (ZFC) Axiomatic Set Theory
	1.4 Basic Concepts of Measure Theory
	1.5 Lebesgue Integral
	1.6 Counting
	1.7 Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Measure
	Exercises
Chapter 2 Basics of Probability
	2.1 Basics of Probability
	2.2 Fuzzy Probability
	2.3 Conditional Probability
	2.4 Independence
	2.5 The Law of Total Probability and Bayes’ Theorem
	Exercises
Chapter 3 Random Variables and Probability Distribution Functions
	3.1 Introduction
	3.2 Discrete Probability Distribution (Mass) Functions (pmf)
	3.3 Moments of a Discrete Random Variable
		3.3.1 Arithmetic Average
		3.3.2 Moments of a Discrete Random Variable
	3.4 Basic Standard Discrete Probability Mass Functions
		3.4.1 Discrete Uniform pmf
		3.4.2 Bernoulli pmf
		3.4.3 Binomial pmf
		3.4.4 Geometric pmf
		3.4.5 Negative Binomial pmf
		3.4.6 Hypergeometric pmf
		3.4.7 Poisson pmf
	3.5 Probability Distribution Function (cdf) for a Continuous Random Variable
	3.6 Moments of a Continuous Random Variable
	3.7 Continuous Moment Generating Function
	3.8 Functions of Random Variables
	3.9 Some Popular Continuous Probability Distribution Functions
		3.9.1 Continuous Uniform Distribution
		3.9.2 Gamma Distribution
		3.9.3 Exponential Distribution
		3.9.4 Beta Distribution
		3.9.5 Erlang Distribution
		3.9.6 Normal Distribution
		3.9.7 χ[sup(2)], Chi-Squared, Distribution
		3.9.8 The F-Distribution
		3.9.9 Student’s t-Distribution
		3.9.10 Weibull Distribution
		3.9.11 Lognormal Distribution
		3.9.12 Logistic Distribution
		3.9.13 Extreme Value Distribution
	3.10 Asymptotic Probabilistic Convergence
	Exercises
Chapter 4 Descriptive Statistics
	4.1 Introduction and History of Statistics
	4.2 Basic Statistical Concepts
		4.2.1 Data Collection
	4.3 Sampling Techniques
	4.4 Tabular and Graphical Techniques in Descriptive Statistics
		4.4.1 Frequency Distribution for Qualitative Data
		4.4.2 Bar Graph
		4.4.3 Pie Chart
		4.4.4 Frequency Distribution for Quantitative Data
		4.4.5 Histogram
		4.4.6 Stem-and-Leaf Plot
		4.4.7 Dot Plot
	4.5 Measures of Central Tendency
	4.6 Measure of Relative Standing
		4.6.1 Percentile
		4.6.2 Quartile
		4.6.3 z-Score
	4.7 More Plots
		4.7.1 Box-and-Whisker Plot
		4.7.2 Scatter Plot
	4.8 Measures of Variability
		4.8.1 Range
		4.8.2 Variance
		4.8.3 Standard Deviation
	4.9 Understanding the Standard Deviation
		4.9.1 The Empirical Rule
		4.9.2 Chebyshev’s Rule
	Exercises
Chapter 5 Inferential Statistics
	5.1 Introduction
	5.2 Estimation and Hypothesis Testing
		5.2.1 Point Estimation
		5.2.2 Interval Estimation
		5.2.3 Hypothesis Testing
	5.3 Comparison of Means and Analysis of Variance (ANOVA)
		5.3.1 Inference about Two Independent Population Means
			5.3.1.1 Confidence Intervals for the Difference in Population Means
			5.3.1.2 Hypothesis Test for the Difference in Population Means
		5.3.2 Confidence Interval for the Difference in Means of Two Populations with Paired Data
		5.3.3 Analysis of Variance (ANOVA)
			5.3.3.1 ANOVA Implementation Steps
			5.3.3.2 One-Way ANOVA
	Exercises
Chapter 6 Nonparametric Statistics
	6.1 Why Nonparametric Statistics?
	6.2 Chi-Square Tests
		6.2.1 Goodness-of-Fit
		6.2.2 Test of Independence
		6.2.3 Test of Homogeneity
	6.3 Single-Sample Nonparametric Statistic
		6.3.1 Single-Sample Sign Test
	6.3 Two-Sample Inference
		6.3.1 Independent Two-Sample Inference Using Mann–Whitney Test
		6.3.2 Dependent Two-Sample Inference Using Wilcoxon Signed-Rank Test
	6.4 Inference Using More Than Two Samples
		6.4.1 Independent Sample Inference Using the Kruskal–Wallis Test
	Exercises
Chapter 7 Stochastic Processes
	7.1 Introduction
	7.2 Random Walk
	7.3 Point Process
	7.4 Classification of States of a Markov Chain/Process
	7.5 Martingales
	7.6 Queueing Processes
		7.6.1 The Simplest Queueing Model, M/M/1
		7.6.2 An M/M/1 Queueing System with Delayed Feedback
			7.6.2.1 Number of Busy Periods
		7.6.3 A MAP Single-Server Service Queueing System
			7.6.3.1 Analysis of the Model
			7.6.3.2 Service Station
			7.6.3.3 Number of Tasks in the Service Station
			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
			7.6.3.5 An Illustrative Example
		7.6.4 Multi-Server Queueing Model, M/M/c
			7.6.4.1 A Stationary Multi-Server Queueing System with Balking and Reneging
			7.6.4.2 Case s= 0 (No Reneging)
			7.6.4.3 Case s= 0 (No Reneging)
	7.7 Birth-and-Death Processes
		7.7.1 Finite Pure Birth
		7.7.2 B-D Process
		7.7.3 Finite Birth-and-Death Process
			7.7.3.1 Analysis
			7.7.3.2 Busy Period
	7.8 Fuzzy Queues/Quasi-B-D
		7.8.1 Quasi-B-D
		7.8.2 A Fuzzy Queueing Model as a QBD
			7.8.2.1 Crisp Model
			7.8.2.2 The Model in Fuzzy Environment
			7.8.2.3 Performance Measures of Interest
	Exercises
Appendix
Bibliography
Index