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The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data. Calculus is assumed as a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.
1. Introduction to Probability.
The History of Probability.
Interpretations of Probability.
Experiments and Events.
The Definition of Probability.
Finite Sample Spaces.
The Probability of a Union of Events.
2. Conditional Probability.
The Definition of Conditional Probability.
The Gambler's Ruin Problem.
3. Random Variables and Distribution.
Random Variables and Discrete Distributions.
The Distribution Function.
Functions of a Random Variable.
Functions of Two or More Random Variables.
The Expectation of a Random Variable.
Properties of Expectations.
The Mean and The Median.
Covariance and Correlation.
The Sample Mean.
5. Special Distributions.
The Bernoulli and Binomial Distributions.
The Hypergeometric Distribution.
The Poisson Distribution.
The Negative Binomial Distribution.
The Normal Distribution.
The Central Limit Theorem.
The Correction for Continuity.
The Gamma Distribution.
The Beta Distribution.
The Multinomial Distribution.
The Bivariate Normal Distribution.
Prior and PosteriorDistributions.
Conjugate Prior Distributions.
Maximum Likelihood Estimators.
Properties of Maximum Likelihood Estimators.
Jointly Sufficient Statistics.
Improving an Estimator.
7. Sampling Distributions of Estimators.
The Sampling Distribution of a Statistic.
The Chi-Square Distribution.
Joint Distribution of the Sample Mean and Sample Variance.
The t Distribution.
Bayesian Analysis of Samples from a Normal Distribution.
8. Testing Hypotheses.
Problems of Testing Hypotheses.
Testing Simple Hypotheses.
Uniformly Most Powerful Tests.
The t Test.
Comparing the Means of Two Normal Distributions.
The F Distribution.
Bayes Test Procedures.
9. Categorical Data and Nonparametric Methods.
Tests of Goodness-of-Fit.
Goodness-of-Fit for Composite Hypotheses.
Tests of Homogeneit.
Sign and Rank Tests.
10. Linear Statistical Models.
The Method of Least Squares.
Statistical Inference in Simple Linear Regression.
Bayesian Inference in Simple Linear Regression.
The General Linear Model and Multiple Regression.
Analysis of Variance.
The Two-Way Layout.
The Two-Way Layout with Replications.
Why is Simulation Useful?
Simulating Specific Distributions.
Markov Chain Monte Carlo.