Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, 4/e
J. Susan Milton,
Radford University - Emeritus Jesse Arnold,
Virginia Polytechnic Institute & State University
ISBN: 007246836x Copyright year: 2003
Table of Contents
1 - Introduction to Probability and Counting 1.1 Interpreting Probabilities 1.2 Sample Spaces and Events 1.3 Permutations and Combinations
Chapter Summary
Exercises
Review Exercises
2 - Some Probability Laws 2.1 Axioms of Probability 2.2 Conditional Probability 2.3 Independence and the Multiplication Rule 2.4 Bayes' Theorem
Chapter Summary
Exercises
Review Exercises
3 - Discrete Distributions 3.1 Random Variables 3.2 Discrete Probability Densities 3.3 Expectation and Distribution Parameters 3.4 Geometric Distribution and the Moment Generating Function 3.5 Binomial Distribution 3.6 Negative Binomial Distribution 3.7 Hypergeometric Distribution 3.8 Poisson Distribution 3.9 Simulating a Discrete Distribution
Chapter Summary
Exercises
Review Exercises
4 - Continuous Distributions 4.1 Continuous Densities 4.2 Expectation and Distribution Parameters 4.3 Gamma, Exponential, and Chi-Squared Distributions 4.4 Normal Distribution 4.5 Normal Probability Rule and Chebyshev's Inequality 4.6 Normal Approximation to the Binomial Distribution 4.7 Weibull Distribution and Reliability 4.8 Transformation of Variables 4.9 Simulating a Continuous Distribution
Chapter Summary
Exercises
Review Exercises
5 - Joint Distributions 5.1 Joint Densities and Independence 5.2 Expectation and Covariance 5.3 Correlation 5.4 Conditional Densities and Regression 5.5 Transformation of Variables
Chapter Summary
Exercises
Review Exercises
6 - Descriptive Statistics 6.1 Random Sampling 6.2 Picturing the Distribution 6.3 Sample Statistics 6.4 Boxplots
Chapter Summary
Exercises
Review Exercises
7 - Estimation 7.1 Point Estimation 7.2 The Method of Moments and Maximum Likelihood 7.3 Functions of Random Variables – Distribution of 7.4 Interval Estimation and the Central Limit Theorem
Chapter Summary
Exercises
Review Exercises
8 - Inferences on the Mean and Variance of a Distribution 8.1 Interval Estimation of Variability 8.2 Estimating the Mean and the Student-t Distribution 8.3 Hypothesis Testing 8.4 Significance Testing 8.5 Hypothesis and Significance Tests on the Mean 8.6 Hypothesis Test on the Variance 8.7 Alternative Nonparametric Methods
Chapter Summary
Exercises
Review Exercises
9 - Inferences on Proportions 9.1 Estimating Proportions 9.2 Testing Hypothesis on a Proportion 9.3 Comparing Two Proportions: Estimation 9.4 Comparing Two Proportions: Hypothesis Testing
Chapter Summary
Exercises
Review Exercises
10 - Comparing Two Means and Two Variances 10.1 Point Estimation: Independent Samples 10.2 Comparing Variances: The F Distribution 10.3 Comparing Means: Variances Equal (Pooled Test) 10.4 Comparing Means: Variances Unequal 10.5 Comparing Means: Paired Data 10.6 Alternative Nonparametric Methods 10.7 A Note on Technology
Chapter Summary
Exercises
Review Exercises
11 - Simple Linear Regression and Correlation 11.1 Model and Parameter Estimation 11.2 Properties of Least-Squares Estimators 11.3 Confidence Interval Estimation and Hypothesis Testing 11.4 Repeated Measurements and Lack of Fit 11.5 Residual Analysis 11.6 Correlation
Chapter Summary
Exercises
Review Exercises
12 - Multiple Linear Regression Models 12.1 Least-Squares Procedures for Model Fitting 12.2 A Matrix Approach to Least Squares 12.3 Properties of the Least-Squares Estimators 12.4 Interval Estimation 12.5 Testing Hypothesis about Model Parameters 12.6 Use of Indicator or "Dummy" Variables 12.7 Criteria for Variable Selection 12.8 Model Transformation and Concluding Remarks
Chapter Summary
Exercises
Review Exercises
13 - Analysis of Variance 13.1 One-Way Classification Fixed-Effects Model 13.2 Comparing Variances 13.3 Pairwise Comparisons 13.4 Testing Contrasts 13.5 Randomized Complete Block Design 13.6 Latin Squares 13.7 Random-Effects Models 13.8 Design Models in Matrix Form 13.9 Alternative Nonparametirc Methods
Chapter Summary
Exercises
Review Exercises
14 - Factorial Experiments 14.1 Two-Factor Analysis of Variance 14.2 Extension to Three Factors 14.3 Random and Mixed Model Factorial Experiments 14.4 2k Factorial Experiments 14.5 2k Factorial Experiments in an Incomplete Block Design 14.6 Fractional Factorial Experiments
Chapter Summary
Exercises
Review Exercises
15 - Categorical Data 15.1 Multinomial Distribution 15.2 Chi-Squared Goodness of Fit Tests 15.3 Testing for Independence 15.4 Comparing Proportions
Chapter Summary
Exercises
Review Exercises
16 - Statistical Quality Control 16.1 Properties of Control Charts 16.2 Shewhart Control Charts for Measurements 16.3 Shewhart Control Charts for Attributes 16.4 Tolerance Limits 16.5 Acceptance Sampling 16.6 Two-Stage Acceptance Sampling 16.7 Extensions in Quality Control
Chapter Summary
Exercises
Review Exercises
Appendix A - Statistical Tables
Appendix B - Answers to Selected Problems
Appendix C - Selected Derivations
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