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What Is Statistics? Introduction | |
Characterizing a Set of Measurements: Graphical Methods | |
Characterizing a Set of Measurements: Numerical Methods | |
How Inferences Are Made | |
Theory and Reality | |
Summary | |
Probability | |
Introduction | |
Probability and Inference | |
A Review of Set Notation | |
A Probabilistic Model for an Experiment: The Discrete Case | |
Calculating the Probability of an Event: The Sample-Point Method | |
Tools for Counting Sample Points | |
Conditional Probability and the Independence of Events | |
Two Laws of Probability | |
Calculating the Probability of an Event: The Event-Composition Methods | |
The Law of Total Probability and Bayes's Rule | |
Numerical Events and Random Variables | |
Random Sampling | |
Summary | |
Discrete Random Variables and Their Probability Distributions | |
Basic Definition | |
The Probability Distribution for Discrete Random Variable | |
The Expected Value of Random Variable or a Function of Random Variable | |
The Binomial Probability Distribution | |
The Geometric Probability Distribution | |
The Negative Binomial Probability Distribution (Optional) | |
The Hypergeometric Probability Distribution | |
Moments and Moment-Generating Functions | |
Probability-Generating Functions (Optional) | |
Tchebysheff's Theorem | |
Summary | |
Continuous Random Variables and Their Probability Distributions | |
Introduction | |
The Probability Distribution for Continuous Random Variable | |
The Expected Value for Continuous Random Variable | |
The Uniform Probability Distribution | |
The Normal Probability Distribution | |
The Gamma Probability Distribution | |
The Beta Probability Distribution | |
Some General Comments | |
Other Expected Values | |
Tchebysheff's Theorem | |
Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional) | |
Summary | |
Multivariate Probability Distributions | |
Introduction | |
Bivariate and Multivariate Probability Distributions | |
Independent Random Variables | |
The Expected Value of a Function of Random Variables | |
Special Theorems | |
The Covariance of Two Random Variables | |
The Expected Value and Variance of Linear Functions of Random Variables | |
The Multinomial Probability Distribution | |
The Bivariate Normal Distribution (Optional) | |
Conditional Expectations | |
Summary | |
Functions of Random Variables | |
Introductions | |
Finding the Probability Distribution of a Function of Random Variables | |
The Method of Distribution Functions | |
The Methods of Transformations | |
Multivariable Transformations Using Jacobians | |
Order Statistics | |
Summary | |
Sampling Distributions and the Central Limit Theorem | |
Introduction | |
Sampling Distributions Related to the Normal Distribution | |
The Central Limit Theorem | |
A Proof of the Central Limit Theorem (Optional) | |
The Normal Approximation to the Binomial Distributions | |
Summary | |
Estimation | |
Introduction | |
The Bias and Mean Square Error of Point Estimators | |
Some Common Unbiased Point Estimators | |
Evaluating the Goodness of Point Estimator | |
Confidence Intervals | |
Large-Sample Confidence Intervals Selecting the Sample Size | |
Small-Sample Confidence Intervals for u and u1-u2 | |
Confidence Intervals for o2 | |
Summary | |
Properties of Point Estimators and Methods of Estimation | |
Introduction | |
Relative Efficiency | |
Consistency | |
Sufficiency | |
The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation | |
The Method of Moments | |
The Method of Maximum Likelihood | |
Some Large-Sample Properties of MLEs (Optional) | |
Summary | |
Hypothesis Testing | |
Introduction | |
Elements of a Statistical Test | |
Common Large-Sample Tests | |
Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test | |
Relationships Between Hypothesis Testing Procedures and Confidence Intervals | |
Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values | |
Some Comments on the Theory of Hypothesis Testing | |
Small-Sample Hypothesis Testing for u and u1-u2 | |
Testing Hypotheses Concerning Variances | |
Power of Test and the Neyman-Pearson Lemma | |
Likelihood Ration Test | |
Summary | |
Linear Models and Estimation by Least Sq | |
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