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### Mathematical Statistics with Applications (Wackerly)

 Author(s) Wackerly, Mendenhall, and Scheaffer Title Mathematical Statistics with Applications Edition Sixth Edition Year 2002 Publisher Duxbury ISBN 0-534-37741-6 Website http://www.cengage.com/us/index.html book link

1. What Is Statistics?
• Introduction.
• Characterizing a Set of Measurements: Graphical Methods.
• Characterizing a Set of Measurements: Numerical Methods.
• Theory and Reality.
• Summary.

2. 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.

3. 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.

4. 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.
• Other Expected Values.
• Tchebysheff''s Theorem.
• Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional).
• Summary.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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 Ratio Test.
• Summary.

11. Linear Models and Estimation by Least Squares.
• Introduction.
• Linear Statistical Models.
• The Method of Least Squares.
• Properties of the Least Squares Estimators for the Simple Linear Regression Model.
• Inference Concerning the Parameters BI.
• Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression.
• Predicting a Particular Value of Y Using Simple Linear Regression. Correlation.
• Some Practical Examples.
• Fitting the Linear Model by Using Matrices.
• Properties of the Least Squares Estimators for the Multiple Linear Regression Model.
• Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression.
• Prediction a Particular Value of Y Using Multiple Regression.
• A Test for H0: Bg+1 + Bg+2 = . = Bk = 0.
• Summary and Concluding Remarks.

12. Considerations in Designing Experiments.
• The Elements Affecting the Information in a Sample.
• Designing Experiment to Increase Accuracy.
• The Matched Pairs Experiment.
• Some Elementary Experimental Designs.
• Summary.

13. The Analysis of Variance.
• Introduction.
• The Analysis of Variance Procedure.
• Comparison of More than Two Means: Analysis of Variance for a One-way Layout.
• An Analysis of Variance Table for a One-Way Layout.
• A Statistical Model of the One-Way Layout.
• Proof of Additivity of the Sums of Squares and E (MST) for a One-Way Layout (Optional).
• Estimation in the One-Way Layout.
• A Statistical Model for the Randomized Block Design.
• The Analysis of Variance for a Randomized Block Design.
• Estimation in the Randomized Block Design.
• Selecting the Sample Size.
• Simultaneous Confidence Intervals for More than One Parameter.
• Analysis of Variance Using Linear Models. Summary.

14. Analysis of Categorical Data.
• A Description of the Experiment.
• The Chi-Square Test.
• A Test of Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test.
• Contingency Tables.
• r x c Tables with Fixed Row or Column Totals.
• Other Applications.
• Summary and Concluding Remarks.

15. Nonparametric Statistics.
• Introduction.
• A General Two-Sampling Shift Model.
• A Sign Test for a Matched Pairs Experiment.
• The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment.
• The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples.
• The Mann-Whitney U Test: Independent Random Samples.
• The Kruskal-Wallis Test for One-Way Layout.
• The Friedman Test for Randomized Block Designs.
• The Runs Test: A Test for Randomness.
• Rank Correlation Coefficient.
• Some General Comments on Nonparametric Statistical Test.

16. Introduction to Bayesian Methods for Inference.
• Introduction.
• Bayesian Priors, Posteriors and Estimators.
• Bayesian Credible Intervals.
• Bayesian Tests of Hypotheses.

Appendix 1. Matrices and Other Useful Mathematical Results.
• Matrices and Matrix Algebra.
• Multiplication of a Matrix by a Real Number.
• Matrix Multiplication.
• Identity Elements.
• The Inverse of a Matrix.
• The Transpose of a Matrix.
• A Matrix Expression for a System of Simultaneous Linear Equations.
• Inverting a Matrix.
• Solving a System of Simultaneous Linear Equations.
• Other Useful Mathematical Results.

Appendix 2. Common Probability Distributions, Means, Variances, and Moment-Generating Functions.
• Discrete Distributions.
• Continuous Distributions.

Appendix 3. Tables.
• Binomial Probabilities.
• Table of e-x. Poisson Probabilities.
• Normal Curve Areas.
• Percentage Points of the t Distributions.
• Percentage Points of the F Distributions.
• Distribution of Function U.
• Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test.
• Distribution of the Total Number of Runs R in Sample Size (n1,n2); P(R < a).
• Critical Values of Pearman's Rank Correlation Coefficient.
• Random Numbers.