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Table of Contents
Preface
1. Summary and Display of Data
2. Probability
3. Discrete Distributions
4. Continuous Distributions
5. Sampling Distribution Theory
6. Estimation
7. Tests of Statistical Hypotheses
8. Linear Models
9. Multivariate Distributions
10. Nonparametric Methods
Appendices
A. A Brief Introduction to Maple
B. The Statistics Supplement to Maple
C Table of Random Numbers
Table of Contents
1. Summary and Display of Data
1.1 Random Number Generators
1.2 Samples, Histograms, and Ogives
1.3 Exploratory Data Analysis
1.4 Graphical Comparisons of Data Sets
1.5 Time Sequences
1.6 Scatter Plots, Least Squares, and Correlation
2. Probability
2.1 Properties of Probability
2.2 Methods of Enumeration
2.3 Conditional Probability
2.4 Independent Events
2.5 Bayes' Formula
3. Discrete Distributions
3.1 Random Variables of the Discrete Type
3.2 Mathematical Expectation
3.3 The Mean, Variance, and Skewness
3.4 The Hypergeometric Distribution
3.5 Bernoulli Trials and The Binomial Distribution
3.6 Geometric and Negative Binomial Distributions
3.7 The Poisson Distribution
3.8 Moment-Generating Functions
4. Continuous Distributions
4.1 Random Variables of the Continuous Type
4.2 The Uniform and Exponential Distributions
4.3 The Gamma and Chi-Square Distributions
4.4 The Normal Distribution
4.5 Other Models
4.6 Mixed Distributions and Censoring
4.7 Simulation
5. Sampling Distribution Theory
5.1 Multivariate Distributions
5.2 Distributions of Sums of Independent Random Variables
5.3 Random Functions Associated with Normal Distributions
5.4 The Central Limit Theorem
5.5 Approximations of Discrete Distributions
5.6 Limiting Moment-Generating Functions
5.7 The t and F Distributions
5.8 Understanding Variability and Control Charts
5.9 Transformations of Random Variables
6. Estimation
6.1 Properties of Estimators
6.2 Confidence Intervals for Means
6.3 Confidence Intervals for Variances
6.4 Confidence Intervals for Proportions
6.5 Sample Size
6.6 Maximum Likelihood Estimation
6.7 Asymptotic Distributions of MLE's
6.8 Chebyshev's Inequality
7. Tests of Statistical Hypotheses
7.1 Tests About Proportions
7.2 Power Function and Sample Size
7.3 Tests About One Mean and One Variance
7.4 Tests of the Equality of Two Variances
7.5 Graphical Methods
7.6 Likelihood Ratio Tests
8. Linear Models
8.1 Tests of the Equality of Several Means
8.2 Two-Factor Analysis of Variance
8.3 Regression Analysis
9. Multivariate Distributions
9.1 The Correlation Coefficient
9.2 Conditional Distributions
9.3 The Bivariate Normal Distribution
9.4 Correlation Analysis
9.5 The Basic Chi-Square Statistic
9.6 Testing Probabilistic Models
9.7 Tests of the Equality of Multinomial Distributions
10. Nonparametric Methods
10.1 Order Statistics
10.2 Confidence Intervals for Percentiles
10.3 Binomial Tests for Percentiles
10.4 The Wilcoxon Test
10.5 Two-Sample Distribution-Free Tests
10.6 Run Test and Test for Randomness
10.7 Kolmogorov-Smirnov Goodness of Fit Test
Appendices
A. A Brief Introduction to Maple
A.1 Basic Syntax
A.2 Maple Expressions
A.3 Assignments and Recall
A.4 Maple Notation
A.5 A Sample Session
A.6 Exercises
B. The Statistics Supplement to Maple
B.1 The List Data Structure
B.2 Procedures for Descriptive Statistics
B.3 Random Sample Generators
B.4 Plotting Routines
B.5 Regression
B.6 p.d.f.s of Some Distributions
B.7 c.d.f.s of Some Distributions
B.8 Percentiles of Some Distributions
B.9 Samples from Sampling Distributions
B.10 Confidence Intervals
B.11 Analysis of Variance
B.12 Goodness of Fit Tests
B.13 Nonparametric Tests
B.14 Miscellaneous Items
C Table of Random Numbers
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