# Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences

4^{th}Edition

Copyright: 2003

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ISBN10: 007246836X | ISBN13: 9780072468366

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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

### Program Details

### 1 Introduction to Probability and Counting

#### 1.1 Interpreting Probabilities

#### 1.2 Sample Spaces and Events

#### 1.3 Permutations and Combinations

### 2 Some Probability Laws

#### 2.1 Axioms of Probability

#### 2.2 Conditional Probability

#### 2.3 Independence and the Multiplication Rule

#### 2.4 Bayes' Theorem

### 3 Discrete Distributions

#### 3.1 Random Variables

#### 3.2 Discrete Probablility 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

### 4 Continuous Distributions

#### 4.1 Continuous Densities

#### 4.2 Expectation and Distribution Parameters

#### 4.3 Gamma Distribution

#### 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

### 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

### 6 Descriptive Statistics

#### 6.1 Random Sampling

#### 6.2 Picturing the Distribution

#### 6.3 Sample Statistics

#### 6.4 Boxplots

### 7 Estimation

#### 7.1 Point Estimation

#### 7.2 The Method of Moments and Maximum Likelihood

#### 7.3 Functions of Random Variables--Distribution of X

#### 7.4 Interval Estimation and the Central Limit Theorem

### 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 Tests

#### 8.7 Alternative Nonparametric Methods

### 9 Inferences on Proportions

#### 9.1 Estimating Proportions

#### 9.2 Testing Hypothesis on a Proportion

#### 9.3 Comparing Two Proportions: Estimation

#### 9.4 Coparing Two Proportions: Hypothesis Testing

### 10 Comparing Two Means and Two Variances

#### 10.1 Point Estimation

#### 10.2 Comparing Variances: The F Distribution

#### 10.3 Comparing Means: Variances Equal (Pooled Test)

#### 10.4 Comparing Means: Variances Unequal

#### 10.5 Compairing Means: Paried Data

#### 10.6 Alternative Nonparametric Methods

#### 10.7 A Note on Technology

### 11 Sample 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

### 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 Hypotheses about Model Parameters

#### 12.6 Use of Indicator or "Dummy" Variables

#### 12.7 Criteria for Variable Selection

#### 12.8 Model Transformation and Concluding Remarks

### 13 Analysis of Variance

#### 13.1 One-Way Classification Fixed-Effects Model

#### 13.2 Comparing Variances

#### 13.3 Pairwise Comparison

#### 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 Nonparametric Methods

### 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 2^k Factorial Experiments

#### 14.5 2^k Factorial Experiments in an Incomplete Block Design

#### 14.6 Fractional Factorial Experiments

### 15 Categorical Data

#### 15.1 Multinomial Distribution

#### 15.2 Chi-Squared Goodness of Fit Tests

#### 15.3 Testing for Independence

#### 15.4 Comparing Proportions

### 16 Statistical Quality Control

#### 16.1 Properties of Control Charts

#### 16.2 Shewart Control Charts for Measurements

#### 16.3 Shewart Control Charts for Attributes

#### 16.4 Tolerance Limits

#### 16.5 Acceptance Sampling

#### 16.6 Two-Stage Acceptance Sampling

#### 16.7 Extensions in Quality Control

#### Appendix A Statistical Tables

#### Appendix B Answers to Selected Problems

#### Appendix C Selected Derivations

### 1 Introduction to Probability and Counting

#### 1.1 Interpreting Probabilities

#### 1.2 Sample Spaces and Events

#### 1.3 Permutations and Combinations

### 2 Some Probability Laws

#### 2.1 Axioms of Probability

#### 2.2 Conditional Probability

#### 2.3 Independence and the Multiplication Rule

#### 2.4 Bayes' Theorem

### 3 Discrete Distributions

#### 3.1 Random Variables

#### 3.2 Discrete Probablility 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

### 4 Continuous Distributions

#### 4.1 Continuous Densities

#### 4.2 Expectation and Distribution Parameters

#### 4.3 Gamma Distribution

#### 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

### 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

### 6 Descriptive Statistics

#### 6.1 Random Sampling

#### 6.2 Picturing the Distribution

#### 6.3 Sample Statistics

#### 6.4 Boxplots

### 7 Estimation

#### 7.1 Point Estimation

#### 7.2 The Method of Moments and Maximum Likelihood

#### 7.3 Functions of Random Variables--Distribution of X

#### 7.4 Interval Estimation and the Central Limit Theorem

### 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 Tests

#### 8.7 Alternative Nonparametric Methods

### 9 Inferences on Proportions

#### 9.1 Estimating Proportions

#### 9.2 Testing Hypothesis on a Proportion

#### 9.3 Comparing Two Proportions: Estimation

#### 9.4 Coparing Two Proportions: Hypothesis Testing

### 10 Comparing Two Means and Two Variances

#### 10.1 Point Estimation

#### 10.2 Comparing Variances: The F Distribution

#### 10.3 Comparing Means: Variances Equal (Pooled Test)

#### 10.4 Comparing Means: Variances Unequal

#### 10.5 Compairing Means: Paried Data

#### 10.6 Alternative Nonparametric Methods

#### 10.7 A Note on Technology

### 11 Sample 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

### 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 Hypotheses about Model Parameters

#### 12.6 Use of Indicator or "Dummy" Variables

#### 12.7 Criteria for Variable Selection

#### 12.8 Model Transformation and Concluding Remarks

### 13 Analysis of Variance

#### 13.1 One-Way Classification Fixed-Effects Model

#### 13.2 Comparing Variances

#### 13.3 Pairwise Comparison

#### 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 Nonparametric Methods

### 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 2^k Factorial Experiments

#### 14.5 2^k Factorial Experiments in an Incomplete Block Design

#### 14.6 Fractional Factorial Experiments

### 15 Categorical Data

#### 15.1 Multinomial Distribution

#### 15.2 Chi-Squared Goodness of Fit Tests

#### 15.3 Testing for Independence

#### 15.4 Comparing Proportions

### 16 Statistical Quality Control

#### 16.1 Properties of Control Charts

#### 16.2 Shewart Control Charts for Measurements

#### 16.3 Shewart Control Charts for Attributes

#### 16.4 Tolerance Limits

#### 16.5 Acceptance Sampling

#### 16.6 Two-Stage Acceptance Sampling

#### 16.7 Extensions in Quality Control

#### Appendix A Statistical Tables

#### Appendix B Answers to Selected Problems

#### Appendix C Selected Derivations

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