Larsen R.J., Marx M.L. Introduction to Mathematical Statistics and Its Applications

Prentice Hall – 2012, 768 p.
ISBN: 0321693949.
Noted for its integration of real-world data and case studies, this text offers sound coverage of the theoretical aspects of mathematical statistics. The authors demonstrate how and when to use statistical methods, while reinforcing the calculus that students have mastered in previous courses. Throughout the Fifth Edition, the authors have added and updated examples and case studies, while also refining existing features that show a clear path from theory to practice.An Overview.
Some Examples.
A Brief History.
A Chapter Summary.
Probability.Sample Spaces and the Algebra of Sets.
The Probability Function.
Conditional Probability.
Independence.
Combinatorics.
Combinatorial Probability.
Taking a Second Look at Statistics (Monte Carlo Techniques).
Random Variables.Binomial and Hypergeometric Probabilities.
Discrete Random Variables.
Continuous Random Variables.
Expected Values.
The Variance.
Joint Densities.
Transforming and Combining Random Variables.
Further Properties of the Mean and Variance.
Order Statistics.
Conditional Densities.
Moment-Generating Functions.
Taking a Second Look at Statistics (Interpreting Means).
Appendix A. Minitab Applications.
Special Distributions.The Poisson Distribution.
The Normal Distribution.
The Geometric Distribution.
The Negative Binomial Distribution.
The Gamma Distribution.
Taking a Second Look at Statistics (Monte Carlo.
Simulations).
Appendix A I. Minitab Applications.
Appendix A II. A Proof of the Central Limit Theorem.
Estimation.Estimating Parameters: The Method of Maximum Likelihood and.
the Method of Moments.
Interval Estimation.
Properties of Estimators.
Minimum-Variance Estimators: The Cramer-Rao Lower.
Bound.
Sufficient Estimators.
Consistency.
Bayesian Estimation.
Taking a Second Look at Statistics (Beyond Classical.
Estimation).
Appendix A. Minitab Applications.
Hypothesis Testing.The Decision Rule.
Testing Binomial Data — H: p = po.
Type I and Type II Errors.
A Notion of Optimality: The Generalized Likelihood Ratio.
Taking a Second Look at Statistics (Statistical Significance versus.
Practical Significance).
Table of Contents v.
Inferences Based on the Normal.
Distribution.
. Introduction.
. Comparing Y−μ.
. Deriving the Distribution of Y−μ.
. Drawing Inferences About μ.
. Drawing Inferences About σ.
. Taking a Second Look at Statistics (Type II Error).
Appendix .A I. Minitab Applications.
Appendix .A II. Some Distribution Results for Y and S.
Appendix .A III. A Proof that the One-Sample t Test is a GLRT.
Appendix .A IV. A Proof of Theorem ..
Types of Data: A Brief Overview.Classifying Data.
Taking a Second Look at Statistics (Samples Are Not.
Valid!).
Two-Sample Inferences.Testing H: μX =μY.
Testing H: σ.
Binomial Data: Testing H: pX = pY.
Confidence Intervals for the Two-Sample Problem.
Taking a Second Look at Statistics (Choosing Samples).
Appendix A I. A Derivation of the Two-Sample t Test (A Proof of.
Theorem ).
Appendix A II. Minitab Applications.
Goodness-of-Fit Tests.The Multinomial Distribution.
Goodness-of-Fit Tests: All Parameters Known.
Goodness-of-Fit Tests: Parameters Unknown.
Contingency Tables.
vi Table of Contents.
Taking a Second Look at Statistics (Outliers).
Appendix A. Minitab Applications.
Regression.The Method of Least Squares.
The Linear Model.
Covariance and Correlation.
The Bivariate Normal Distribution.
Taking a Second Look at Statistics (How Not to Interpret.
the Sample Correlation Coefficient).
Appendix A I. Minitab Applications.
Appendix A II. A Proof of Theorem.
The Analysis of Variance.The F Test.
Multiple Comparisons: Tukey’s Method.
Testing Subhypotheses with Contrasts.
Data Transformations.
Taking a Second Look at Statistics (Putting the Subject of.
Statistics Together — The Contributions of Ronald A. Fisher).
Appendix A I. Minitab Applications.
Appendix A II. A Proof of Theorem.
Appendix A III. The Distribution of SSTR/(k–).
SSE/(n–k) When H is True.
Randomized Block Designs.The F Test for a Randomized Block Design.
The Paired t Test.
Taking a Second Look at Statistics (Choosing between a.
Two-Sample t Test and a Paired t Test).
Appendix A. Minitab Applications.
Nonparametric Statistics.The Sign Test.
Table of Contents vii.
Wilcoxon Tests.
The Kruskal-Wallis Test.
The Friedman Test.
Testing for Randomness.
Taking a Second Look at Statistics (Comparing Parametric.
and Nonparametric Procedures).
Appendix A. Minitab Applications.
Appendix: Statistical Tables.
Answers to Selected Odd-Numbered Questions.