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

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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