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

4^{th}Edition

ISBN10: 007246836X

ISBN13: 9780072468366

Copyright: 2003

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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.

### 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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