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

1 Introduction to Probability and Counting1.1 Interpreting Probabilities1.2 Sample Spaces and Events1.3 Permutations and Combinations2 Some Probability Laws2.1 Axioms of Probability2.2 Conditional Probability2.3 Independence and the Multiplication Rule2.4 Bayes' Theorem3 Discrete Distributions3.1 Random Variables3.2 Discrete Probablility Densities3.3 Expectation and Distribution Parameters3.4 Geometric Distribution and the Moment Generating Function3.5 Binomial Distribution3.6 Negative Binomial Distribution3.7 Hypergeometric Distribution3.8 Poisson Distribution4 Continuous Distributions4.1 Continuous Densities4.2 Expectation and Distribution Parameters4.3 Gamma Distribution4.4 Normal Distribution4.5 Normal Probability Rule and Chebyshev's Inequality4.6 Normal Approximation to the Binomial Distribution4.7 Weibull Distribution and Reliability4.8 Transformation of Variables4.9 Simulating a Continuous Distribution5 Joint Distributions5.1 Joint Densities and Independence5.2 Expectation and Covariance5.3 Correlation5.4 Conditional Densities and Regression5.5 Transformation of Variables6 Descriptive Statistics6.1 Random Sampling6.2 Picturing the Distribution6.3 Sample Statistics6.4 Boxplots7 Estimation7.1 Point Estimation7.2 The Method of Moments and Maximum Likelihood7.3 Functions of Random Variables--Distribution of X 7.4 Interval Estimation and the Central Limit Theorem8 Inferences on the Mean and Variance of a Distribution8.1 Interval Estimation of Variability8.2 Estimating the Mean and the Student-t Distribution8.3 Hypothesis Testing8.4 Significance Testing8.5 Hypothesis and Significance Tests on the Mean8.6 Hypothesis Tests8.7 Alternative Nonparametric Methods9 Inferences on Proportions9.1 Estimating Proportions9.2 Testing Hypothesis on a Proportion9.3 Comparing Two Proportions: Estimation9.4 Coparing Two Proportions: Hypothesis Testing10 Comparing Two Means and Two Variances10.1 Point Estimation10.2 Comparing Variances: The F Distribution10.3 Comparing Means: Variances Equal (Pooled Test)10.4 Comparing Means: Variances Unequal10.5 Compairing Means: Paried Data10.6 Alternative Nonparametric Methods10.7 A Note on Technology11 Sample Linear Regression and Correlation11.1 Model and Parameter Estimation11.2 Properties of Least-Squares Estimators11.3 Confidence Interval Estimation and Hypothesis Testing11.4 Repeated Measurements and Lack of Fit11.5 Residual Analysis11.6 Correlation12 Multiple Linear Regression Models12.1 Least-Squares Procedures for Model Fitting12.2 A Matrix Approach to Least Squares12.3 Properties of the Least-Squares Estimators12.4 Interval Estimation12.5 Testing Hypotheses about Model Parameters12.6 Use of Indicator or "Dummy" Variables12.7 Criteria for Variable Selection12.8 Model Transformation and Concluding Remarks13 Analysis of Variance13.1 One-Way Classification Fixed-Effects Model13.2 Comparing Variances13.3 Pairwise Comparison13.4 Testing Contrasts13.5 Randomized Complete Block Design13.6 Latin Squares13.7 Random-Effects Models13.8 Design Models in Matrix Form13.9 Alternative Nonparametric Methods14 Factorial Experiments14.1 Two-Factor Analysis of Variance14.2 Extension to Three Factors14.3 Random and Mixed Model Factorial Experiments14.4 2^k Factorial Experiments 14.5 2^k Factorial Experiments in an Incomplete Block Design 14.6 Fractional Factorial Experiments15 Categorical Data15.1 Multinomial Distribution15.2 Chi-Squared Goodness of Fit Tests15.3 Testing for Independence15.4 Comparing Proportions16 Statistical Quality Control16.1 Properties of Control Charts16.2 Shewart Control Charts for Measurements16.3 Shewart Control Charts for Attributes16.4 Tolerance Limits16.5 Acceptance Sampling16.6 Two-Stage Acceptance Sampling16.7 Extensions in Quality ControlAppendix A Statistical TablesAppendix B Answers to Selected ProblemsAppendix C Selected Derivations