Mathematical Statistics with Applications
by Wackerly, Dennis; Mendenhall, William; Scheaffer, Richard
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Summary
Table of Contents
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 SamplePoint Method  
Tools for Counting Sample Points  
Conditional Probability and the Independence of Events  
Two Laws of Probability  
Calculating the Probability of an Event: The EventComposition 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 MomentGenerating Functions  
ProbabilityGenerating 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  
LargeSample Confidence Intervals Selecting the Sample Size  
SmallSample Confidence Intervals for u and u1u2  
Confidence Intervals for o2  
Summary  
Properties of Point Estimators and Methods of Estimation  
Introduction  
Relative Efficiency  
Consistency  
Sufficiency  
The RaoBlackwell Theorem and MinimumVariance Unbiased Estimation  
The Method of Moments  
The Method of Maximum Likelihood  
Some LargeSample Properties of MLEs (Optional)  
Summary  
Hypothesis Testing  
Introduction  
Elements of a Statistical Test  
Common LargeSample 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 pValues  
Some Comments on the Theory of Hypothesis Testing  
SmallSample Hypothesis Testing for u and u1u2  
Testing Hypotheses Concerning Variances  
Power of Test and the NeymanPearson Lemma  
Likelihood Ration Test  
Summary  
Linear Models and Estimation by Least Sq  
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