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1. Probability
1.1 Properties of Probability
1.2 Methods of Enumeration
1.3 Conditional Probability
1.4 Independent Events
1.5 Bayes’ Theorem
2. Discrete Distributions
2.1 Random Variables of the Discrete Type
2.2 Mathematical Expectation
2.3 Special Mathematical Expectations
2.4 The Binomial Distribution
2.5 The Hypergeometric Distribution
2.6 The Negative Binomial Distribution
2.7 The Poisson Distribution
3. Continuous Distributions
3.1 Random Variables of the Continuous Type
3.2 The Exponential, Gamma, and Chi-Square Distributions
3.3 The Normal Distribution
3.4 Additional Models
4. Bivariate Distributions
4.1 Bivariate Distributions of the Discrete Type
4.2 The Correlation Coefficient
4.3 Conditional Distributions
4.4 Bivariate Distributions of the Continuous Type
4.5 The Bivariate Normal Distribution
5. Distributions of Functions of Random Variables
5.1 Functions of One Random Variable
5.2 Transformations of Two Random Variables
5.3 Several Independent Random Variables
5.4 The Moment-Generating Function Technique
5.5 Random Functions Associated with Normal Distributions
5.6 The Central Limit Theorem
5.7 Approximations for Discrete Distributions
5.8 Chebyshev’s Inequality and Convergence in Probability
5.9 Limiting Moment-Generating Functions
6. Point Estimation
6.1 Descriptive Statistics
6.2 Exploratory Data Analysis
6.3 Order Statistics
6.4 Maximum Likelihood and Method of Moments Estimation
6.5 A Simple Regression Problem
6.6 Asymptotic Distributions of Maximum Likelihood Estimators
6.7 Sufficient Statistics
6.8 Bayesian Estimation
7. Interval Estimation
7.1 Confidence Intervals for Means
7.2 Confidence Intervals for the Difference of Two Means
7.3 Confidence Intervals for Proportions
7.4 Sample Size
7.5 Distribution-Free Confidence Intervals for Percentiles
7.6 More Regression
7.7 Resampling Methods
8. Tests of Statistical Hypotheses
8.1 Tests About One Mean
8.2 Tests of the Equality of Two Means
8.3 Tests for Variances
8.4 Tests About Proportions
8.5 Some Distribution-Free Tests
8.6 Power of a Statistical Test
8.7 Best Critical Regions
8.8 Likelihood Ratio Tests
9. More Tests
9.1 Chi-Square Goodness-of-Fit Tests
9.2 Contingency Tables
9.3 One-Factor Analysis of Variance
9.4 Two-Way Analysis of Variance
9.5 General Factorial and 2k Factorial Designs
9.6 Tests Concerning Regression and Correlation
9.7 Statistical Quality Control
APPENDICES
A. References
B. Tables
C. Answers to Odd-Numbered Exercises
D. Review of Selected Mathematical Techniques
D.1 Algebra of Sets
D.2 Mathematical Tools for the Hypergeometric Distribution
D.3 Limits
D.4 Infinite Series
D.5 Integration
D.6 Multivariate Calculus
Index