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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