Preface 1 Introduction 1.1 Introduction 1.2 Combinatorial Methods 1.3 Binomial Coefficients 1.4 The Theory in Practice 2 Probability 2.1 Introduction 2.2 Sample Spaces 2.3 Events 2.4 The Probability of an Event 2.5 Some Rules of Probability 2.6 Conditional Probability 2.7 Independent Events 2.8 Bayes'' Theorem 2.9 The Theory in Practice 3 Probability Distributions and Probability Densities 3.1 Random Variables 3.2 Probability Distributions 3.3 Continuous Random Variables 3.4 Probability Density Functions 3.5 Multivariate Distributions 3.6 Marginal Distributions 3.7 Conditional Distributions 3.8 The Theory in Practice 4 Mathematical Expectation 4.1 Introduction 4.2 The Expected Value of a Random Variable 4.3 Moments 4.4 Chebyshev''s Theorem 4.5 Moment-Generating Functions 4.6 Product Moments 4.7 Moments of Linear Combinations of Random Variables 4.8 Conditional Expectations 4.9 The Theory in Practice 5 Special Probability Distributions 5.1 Introduction 5.2 The Discrete Uniform Distribution 5.3 The Bernoulli Distribution 5.4 The Binomial Distribution 5.5 The Negative Binomial and Geometric Distributions 5.6 The Hypergeometric Distribution 5.7 The Poisson Distribution 5.8 The Multinomial Distribution 5.9 The Multivariate Hypergeometric Distribution 5.10 The Theory in Practice 6 Special Probability Densities 6.1 Introduction 6.2 The Uniform Distribution 6.3 The Gamma, Exponential, and Chi-Square Distributions 6.4 The Beta Distribution 6.5 The Normal Distribution 6.6 The Normal Approximation to the Binomial Distribution 6.7 The Bivariate Normal Distribution 6.8 The Theory in Practice 7 Functions of Random Variables 7.1 Introduction 7.2 Distribution Function Technique 7.3 Transformation Technique: One Variable 7.4 Transformation Technique: Several Variables 7.5 Moment-Generating Function Technique 7.6 The Theory in Application 8 Sampling Distributions 8.1 Introduction 8.2 The Distribution of the Mean 8.3 The Distribution of the Mean: Finite Populations 8.4 The Chi-Square Distribution 8.5 The t Distribution 8.6 The F Distribution 8.7 Order Statistics 8.8 The Theory in Practice 9 Decision Theory 9.1 Introduction 9.2 The Theory of Games 9.3 Statistical Games 9.4 Decision Criteria 9.5 The Minimax Criterion 9.6 The Bayes Criterion 9.7 The Theory in Practice 10 Point Estimation 10.1 Introduction 10.2 Unbiased Estimators 10.3 Efficiency 10.4 Consistency 10.5 Sufficiency 10.6 Robustness 10.7 The Method of Moments 10.8 The Method of Maximum Likelihood 10.9 Bayesian Estimation 10.10 The Theory in Practice 11 Interval Estimation 11.1 Introduction 11.2 The Estimation of Means 11.3 The Estimation of Differences Between Means 11.4 The Estimation of Proportions 11.5 The Estimation of Differences Between Proportions 11.6 The Estimation of Variances 11.7 The Estimation of the Ratio of Two Variances 11.8 The Theory in Practice 12 Hypothesis Testing 12.1 Introduction 12.2 Testing a Statistical Hypothesis 12.3 Losses and Risks 12.4 The Neyman-Pearson Lemma 12.5 The Power Function of a Test 12.6 Likelihood Ratio Tests 12.7 The Theory in Practice 13 Tests of Hypothesis Involving Means, Variances,and Proportions 13.1 Introduction 13.2 Tests Concerning Means 13.3 Tests Concerning Differences Between Means 13.4 Tests Concerning Variances 13.5 Tests Concerning Proportions 13.6 Tests Concerning Differences Among k Proportions 13.7 The Analysis of an r x c Table 13.8 Goodness of Fit 13.9 The Theory in Practice 14 Regression and Correlation 14.1 Introduction 14.2 Linear Regression 14.3 The Method of Least Squares 14.4 Normal Regression Analysis 14.5 Normal Correlation Analysis 14.6 Multiple Linear Regression 14.7 Multiple Linear Regression Matrix Notation 14.8 The Theory in Practice 15 Design and Analysis of Experiments 15.1 Introduction 15.2 One-Way Designs 15.3 Randomized-Block Designs 15.4 Factorial Experiments 15.5 Multiple Comparisons 15.6 Other Experimental Designs 15.7 The Theory in Practice 16 Nonparametrie Tests 16.1 Introduction 16.2 The Sign Test 16.3 The Signed-Rank Test 16.4 Rank-Sum Tests: The U Test 16.5 Rank-Sum Tests: The H Test 16.6 Tests Based on Runs 16.7 The Rank Correlation Coefficient 16.8 The Theory in Practice APPENDICES A Sums and Products A.1 Rules for Sums and Products A.2 Special Sums B Special Probability Distributions B.1 Bernoulli Distribution B.2 Binomial Distribution B.3 Discrete Uniform Distribution Special Case B.4 Geometric Distribution B.5 Hypergeometric Distribution B.6 Negative Binomial Distribution B.7 Poisson Distribution C Special Probability Densities C.1 Beta Distribution C.2 Cauchy Distribution C.3 Chi-Square Distribution C.4 Exponential Distribution C.5 F Distribution C.6 Gamma Distribution C.7 Normal Distribution C.8 t Distribution Student''s-t Distribution C.9 Uniform Distribution Rectangular Distribution Statistical Tables Answers to Odd-Numbered Exercises Index
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