Brief Course in Mathematical Statistics, A

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Brief Course in Mathematical Statistics, A

• Preface
• 1. Probability
• 1.1 Basic Concepts
• 1.2 Methods of Enumeration
• 1.3 Conditional Probability
• 1.4 Independent Events
• 1.5 Bayes's Theorem
• Chapter One Comments
• 2. Discrete Distributions
• 2.1 Discrete Probability Distributions
• 2.2 Expectations
• 2.3 Special Discrete Distributions
• 2.4 Estimation
• 2.5 Linear Functions of Independent Random Variables
• 2.6 Multivariate Discrete Distributions
• Chapter Two Comments
• 3. Continuous Distributions
• 3.1 Descriptive Statistics and EDA
• 3.2 Continuous Probability Distributions
• 3.3 Special Continuous Distributions
• 3.4 The Normal Distribution
• 3.5 Estimation in the Continuous Case
• 3.6 The Central Limit Theorem
• 3.7 Approximations for Discrete Distributions
• Chapter Three Comemnts
• 4. Applications of Statistical Inference
• 4.1 Summary of Necessary Theoretical Results
• 4.2 Confidence Intervals Using X2 F,and T
• 4.3 Confidence Intervals and Tests of Hypotheses
• 4.4 Basic Tests Concerning One Parameter
• 4.5 Tests of the Equality of Two Parameters
• 4.6 Simple Linear Regression
• 4.7 More on Linear Regression
• 4.8 One-Factor Analysis of Variance
• 4.9 Distribution-Free Confidence and Tolerance Intervals
• 4.10 Chi-Square Goodness of Fit Tests
• 4.11 Contingency Tables
• Chapter Four Comments
• 5. Computer Oriented Techniques
• 5.1 Computation of Statistics
• 5.2 Computer Algebra Systems
• 5.3 Simulation
• 5.4 Resampling
• Chapter Five Comments
• 6. Some Sampling Distribution Theory
• 6.1 Moment-Generation Function Technique
• 6.2 M.G.F of Linear Functions
• 6.3 Limiting Moment-Generating Functions
• 6.4 Use of Order Statistics in Non-regular Cases
• Chapter Six Comments