Introduction to Probability and Statistics for Engineers and Scientists

Contents xi

• Chapter 1 Introduction to Statistics Preface................................................................... xiii
  
  
  • 1.1Introduction
  
  
  • 1.2Data Collection and Descriptive Statistics
  
  
  • 1.3Inferential Statistics and Probability Models
  
  
  • 1.4Populations and Samples
  
  
  • 1.5A Brief History of Statistics
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 2 Descriptive Statistics
  
  
  • 2.1Introduction
  
  
  • 2.2Describing Data Sets
    
    
    • 2.2.1 Frequency Tables and Graphs
    
    
    • 2.2.2 Relative Frequency Tables and Graphs..............................
    
    
    • 2.2.3 Grouped Data, Histograms, Ogives, and Stem and Leaf Plots...........
    
    
    
    
  
  
  • 2.3Summarizing Data Sets
    
    
    • 2.3.1 Sample Mean, Sample Median, and Sample Mode....................
    
    
    • 2.3.2 Sample Variance and Sample Standard Deviation.....................
    
    
    • 2.3.3 Sample Percentiles and Box Plots
    
    
    
    
  
  
  • 2.4Chebyshev’s Inequality
  
  
  • 2.5Normal Data Sets
  
  
  • 2.6Paired Data Sets and the Sample Correlation Coefficient
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 3 Elements of Probability
  
  
  • 3.1Introduction
  
  
  • 3.2Sample Space and Events
  
  
  • 3.3Venn Diagrams and the Algebra of Events
  
  
  • 3.4Axioms of Probability
  
  
  • 3.5Sample Spaces Having Equally Likely Outcomes
  
  
  • 3.6Conditional Probability
  
  
  • 3.7Bayes’ Formula
    
    
    • 3.8Independent Events viii Contents
      
      
      • Problems..........................................................
      
      
      
      
    
    
    
    
  
  
  
  


• Chapter 4 Random Variables and Expectation
  
  
  • 4.1Random Variables
  
  
  • 4.2Types of Random Variables
  
  
  • 4.3Jointly Distributed Random Variables
    
    
    • 4.3.1 Independent Random Variables
    
    
    • *4.3.2 Conditional Distributions
    
    
    
    
  
  
  • 4.4Expectation
  
  
  • 4.5Properties of the Expected Value
    
    
    • 4.5.1 Expected Value of Sums of Random Variables
    
    
    
    
  
  
  • 4.6Variance
  
  
  • 4.7Covariance and Variance of Sums of Random Variables
  
  
  • 4.8Moment Generating Functions
  
  
  • 4.9Chebyshev’s Inequality and the Weak Law of Large Numbers
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 5 Special Random Variables
  
  
  • 5.1The Bernoulli and Binomial Random Variables
    
    
    • 5.1.1 Computing the Binomial Distribution Function
    
    
    
    
  
  
  • 5.2The Poisson Random Variable
    
    
    • 5.2.1 Computing the Poisson Distribution Function
    
    
    
    
  
  
  • 5.3The Hypergeometric Random Variable
  
  
  • 5.4The Uniform Random Variable
  
  
  • 5.5Normal Random Variables
  
  
  • 5.6Exponential Random Variables
    
    
    • *5.6.1 The Poisson Process
    
    
    
    
  
  
  • *5.7The Gamma Distribution
    
    
    • 5.8Distributions Arising from the Normal
      
      
      • 5.8.1 The Chi-Square Distribution
        
        
        • Variables *5.8.1.1The Relation Between Chi-Square and Gamma Random
        
        
        
        
      
      
      • 5.8.2 Thet-Distribution
      
      
      • 5.8.3 TheF-Distribution..............................................
      
      
      
      
    
    
    
    
  
  
  • *5.9The Logistics Distribution
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 6 Distributions of Sampling Statistics
  
  
  • 6.1Introduction
  
  
  • 6.2The Sample Mean
  
  
  • 6.3The Central Limit Theorem
    
    
    • 6.3.1 Approximate Distribution of the Sample Mean Contents ix
    
    
    • 6.3.2 How Large a Sample is Needed?
    
    
    
    
  
  
  • 6.4The Sample Variance
  
  
  • 6.5Sampling Distributions from a Normal Population
    
    
    • 6.5.1 Distribution of the Sample Mean
    
    
    • 6.5.2 Joint Distribution ofXandS
    
    
    
    
  
  
  • 6.6Sampling from a Finite Population
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 7 Parameter Estimation
  
  
  • 7.1Introduction
  
  
  • 7.2Maximum Likelihood Estimators
    
    
    • *7.2.1 Estimating Life Distributions
    
    
    
    
  
  
  • 7.3Interval Estimates
    
    
    • Unknown 7.3.1 Confidence Interval for a Normal Mean When the Variance is
    
    
    • 7.3.2 Confidence Intervals for the Variances of a Normal Distribution
    
    
    
    
  
  
  • 7.4Estimating the Difference in Means of Two Normal Populations
    
    
    • Random Variable 7.5Approximate Confidence Interval for the Mean of a Bernoulli
    
    
    
    
  
  
  • *7.6Confidence Interval of the Mean of the Exponential Distribution
  
  
  • *7.7Evaluating a Point Estimator
  
  
  • *7.8The Bayes Estimator
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 8 Hypothesis Testing
  
  
  • 8.1Introduction
  
  
  • 8.2Significance Levels
  
  
  • 8.3Tests Concerning the Mean of a Normal Population
    
    
    • 8.3.1 Case of Known Variance
    
    
    • 8.3.2 Case of Unknown Variance: Thet-Test.............................
    
    
    
    
  
  
  • 8.4Testing the Equality of Means of Two Normal Populations
    
    
    • 8.4.1 Case of Known Variances
    
    
    • 8.4.2 Case of Unknown Variances
    
    
    • 8.4.3 Case of Unknown and Unequal Variances...........................
    
    
    • 8.4.4 The Pairedt-Test
    
    
    
    
  
  
  • 8.5Hypothesis Tests Concerning the Variance of a Normal Population
    
    
    • Populations 8.5.1 Testing for the Equality of Variances of Two Normal
    
    
    
    
  
  
  • 8.6Hypothesis Tests in Bernoulli Populations
    
    
    • Populations 8.6.1 Testing the Equality of Parameters in Two Bernoulli
    
    
    
    
  
  
  • 8.7Tests Concerning the Mean of a Poisson Distribution x Contents
    
    
    • 8.7.1 Testing the Relationship Between Two Poisson Parameters.............
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 9 Regression
  
  
  • 9.1Introduction
  
  
  • 9.2Least Squares Estimators of the Regression Parameters
  
  
  • 9.3Distribution of the Estimators
  
  
  • 9.4Statistical Inferences about the Regression Parameters
    
    
    • 9.4.1 Inferences Concerningβ
      
      
      • 9.4.1.1Regression to the Mean
      
      
      
      
    
    
    • 9.4.2 Inferences Concerningα
    
    
    • 9.4.3 Inferences Concerning the Mean Responseα+βx
    
    
    • 9.4.4 Prediction Interval of a Future Response
    
    
    • 9.4.5 Summary of Distributional Results.................................
    
    
    • Coefficient 9.5The Coefficient of Determination and the Sample Correlation
    
    
    
    
  
  
  • 9.6Analysis of Residuals: Assessing the Model
  
  
  • 9.7Transforming to Linearity
  
  
  • 9.8Weighted Least Squares
  
  
  • 9.9Polynomial Regression
  
  
  • *9.10Multiple Linear Regression
    
    
    • 9.10.1 Predicting Future Responses
    
    
    • 9.11Logistic Regression Models for Binary Output Data
      
      
      • Problems.........................................................
      
      
      
      
    
    
    
    
  
  
  
  


• Chapter 10 Analysis of Variance
  
  
  • 10.1 Introduction
  
  
  • 10.2 An Overview
  
  
  • 10.3 One-Way Analysis of Variance
    
    
    • 10.3.1 Multiple Comparisons of Sample Means
    
    
    • 10.3.2 One-Way Analysis of Variance with Unequal Sample Sizes
      
      
      • Estimation 10.4 Two-Factor Analysis of Variance: Introduction and Parameter
      
      
      
      
    
    
    
    
  
  
  • 10.5 Two-Factor Analysis of Variance: Testing Hypotheses
  
  
  • 10.6 Two-Way Analysis of Variance with Interaction
    
    
    • Problems
    
    
    
    
  
  
  
  


• Chapter 11 Goodness of Fit Tests and Categorical Data Analysis
  
  
  • 11.1 Introduction
  
  
  • 11.2 Goodness of Fit Tests When all Parameters are Specified
    
    
    • 11.2.1 Determining the Critical Region by Simulation
    
    
    
    
  
  
  • 11.3 Goodness of Fit Tests When Some Parameters are Unspecified
  
  
  • 11.4 Tests of Independence in Contingency Tables
    
    
    • Marginal Totals 11.5 Tests of Independence in Contingency Tables Having Fixed
    
    
    • Data *11.6 The Kolmogorov–Smirnov Goodness of Fit Test for Continuous
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 12 Nonparametric Hypothesis Tests............................
  
  
  • 12.1 Introduction
  
  
  • 12.2 The Sign Test
  
  
  • 12.3 The Signed Rank Test
  
  
  • 12.4 The Two-Sample Problem
    
    
    • 12.4.1 The Classical Approximation and Simulation
    
    
    
    
  
  
  • 12.5 The Runs Test for Randomness
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 13 Quality Control.............................................
  
  
  • 13.1 Introduction
  
  
  • 13.2 Control Charts for Average Values: TheX-Control Chart
    
    
    • 13.2.1 Case of Unknownμandσ
    
    
    
    
  
  
  • 13.3 S-Control Charts
  
  
  • 13.4 Control Charts for the Fraction Defective
  
  
  • 13.5 Control Charts for Number of Defects
    
    
    • Mean 13.6 Other Control Charts for Detecting Changes in the Population
    
    
    • 13.6.1 Moving-Average Control Charts
    
    
    • 13.6.2 Exponentially Weighted Moving-Average Control Charts
    
    
    • 13.6.3 Cumulative Sum Control Charts
    
    
    • Problems..........................................................
    
    
    
    
  
  
  
  


• Chapter 14* Life Testing
  
  
  • 14.1 Introduction
  
  
  • 14.2 Hazard Rate Functions
  
  
  • 14.3 The Exponential Distribution in Life Testing
    
    
    • 14.3.1 Simultaneous Testing — Stopping at therth Failure
    
    
    • 14.3.2 Sequential Testing
    
    
    • 14.3.3 Simultaneous Testing — Stopping by a Fixed Time
    
    
    • 14.3.4 The Bayesian Approach
    
    
    
    
  
  
  • 14.4 A Two-Sample Problem
  
  
  • 14.5 The Weibull Distribution in Life Testing
    
    
    • 14.5.1 Parameter Estimation by Least Squares
    
    
    • Problems..........................................................
      
      
      • Appendix of Tables
      
      
      
      
    
    
    
    
  
  
  
  


• Index