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

<H3>1 Introduction to Probability and Counting<H4>1.1 Interpreting Probabilities<H4>1.2 Sample Spaces and Events<H4>1.3 Permutations and Combinations<H3>2 Some Probability Laws<H4>2.1 Axioms of Probability<H4>2.2 Conditional Probability<H4>2.3 Independence and the Multiplication Rule<H4>2.4 Bayes' Theorem<H3>3 Discrete Distributions<H4>3.1 Random Variables<H4>3.2 Discrete Probablility Densities<H4>3.3 Expectation and Distribution Parameters<H4>3.4 Geometric Distribution and the Moment Generating Function<H4>3.5 Binomial Distribution<H4>3.6 Negative Binomial Distribution<H4>3.7 Hypergeometric Distribution<H4>3.8 Poisson Distribution<H3>4 Continuous Distributions<H4>4.1 Continuous Densities<H4>4.2 Expectation and Distribution Parameters<H4>4.3 Gamma Distribution<H4>4.4 Normal Distribution<H4>4.5 Normal Probability Rule and Chebyshev's Inequality<H4>4.6 Normal Approximation to the Binomial Distribution<H4>4.7 Weibull Distribution and Reliability<H4>4.8 Transformation of Variables<H4>4.9 Simulating a Continuous Distribution<H3>5 Joint Distributions<H4>5.1 Joint Densities and Independence<H4>5.2 Expectation and Covariance<H4>5.3 Correlation<H4>5.4 Conditional Densities and Regression<H4>5.5 Transformation of Variables<H3>6 Descriptive Statistics<H4>6.1 Random Sampling<H4>6.2 Picturing the Distribution<H4>6.3 Sample Statistics<H4>6.4 Boxplots<H3>7 Estimation<H4>7.1 Point Estimation<H4>7.2 The Method of Moments and Maximum Likelihood<H4>7.3 Functions of Random Variables--Distribution of X <H4>7.4 Interval Estimation and the Central Limit Theorem<H3>8 Inferences on the Mean and Variance of a Distribution<H4>8.1 Interval Estimation of Variability<H4>8.2 Estimating the Mean and the Student-t Distribution<H4>8.3 Hypothesis Testing<H4>8.4 Significance Testing<H4>8.5 Hypothesis and Significance Tests on the Mean<H4>8.6 Hypothesis Tests<H4>8.7 Alternative Nonparametric Methods<H3>9 Inferences on Proportions<H4>9.1 Estimating Proportions<H4>9.2 Testing Hypothesis on a Proportion<H4>9.3 Comparing Two Proportions: Estimation<H4>9.4 Coparing Two Proportions: Hypothesis Testing<H3>10 Comparing Two Means and Two Variances<H4>10.1 Point Estimation<H4>10.2 Comparing Variances: The F Distribution<H4>10.3 Comparing Means: Variances Equal (Pooled Test)<H4>10.4 Comparing Means: Variances Unequal<H4>10.5 Compairing Means: Paried Data<H4>10.6 Alternative Nonparametric Methods<H4>10.7 A Note on Technology<H3>11 Sample Linear Regression and Correlation<H4>11.1 Model and Parameter Estimation<H4>11.2 Properties of Least-Squares Estimators<H4>11.3 Confidence Interval Estimation and Hypothesis Testing<H4>11.4 Repeated Measurements and Lack of Fit<H4>11.5 Residual Analysis<H4>11.6 Correlation<H3>12 Multiple Linear Regression Models<H4>12.1 Least-Squares Procedures for Model Fitting<H4>12.2 A Matrix Approach to Least Squares<H4>12.3 Properties of the Least-Squares Estimators<H4>12.4 Interval Estimation<H4>12.5 Testing Hypotheses about Model Parameters<H4>12.6 Use of Indicator or "Dummy" Variables<H4>12.7 Criteria for Variable Selection<H4>12.8 Model Transformation and Concluding Remarks<H3>13 Analysis of Variance<H4>13.1 One-Way Classification Fixed-Effects Model<H4>13.2 Comparing Variances<H4>13.3 Pairwise Comparison<H4>13.4 Testing Contrasts<H4>13.5 Randomized Complete Block Design<H4>13.6 Latin Squares<H4>13.7 Random-Effects Models<H4>13.8 Design Models in Matrix Form<H4>13.9 Alternative Nonparametric Methods<H3>14 Factorial Experiments<H4>14.1 Two-Factor Analysis of Variance<H4>14.2 Extension to Three Factors<H4>14.3 Random and Mixed Model Factorial Experiments<H4>14.4 2^k Factorial Experiments <H4>14.5 2^k Factorial Experiments in an Incomplete Block Design <H4>14.6 Fractional Factorial Experiments<H3>15 Categorical Data<H4>15.1 Multinomial Distribution<H4>15.2 Chi-Squared Goodness of Fit Tests<H4>15.3 Testing for Independence<H4>15.4 Comparing Proportions<H3>16 Statistical Quality Control<H4>16.1 Properties of Control Charts<H4>16.2 Shewart Control Charts for Measurements<H4>16.3 Shewart Control Charts for Attributes<H4>16.4 Tolerance Limits<H4>16.5 Acceptance Sampling<H4>16.6 Two-Stage Acceptance Sampling<H4>16.7 Extensions in Quality Control<H4>Appendix A Statistical Tables<H4>Appendix B Answers to Selected Problems<H4>Appendix C Selected Derivations