Modern Mathematical Statistics With Applications

Purpose......Page 6
Recommended Coverage......Page 7
Acknowledgements......Page 8
A Final Thought......Page 9
Contents......Page 10
1.1 The Language of Statistics......Page 14
1.2 Graphical Methods in Descriptive Statistics......Page 22
1.3 Measures of Center......Page 38
1.4 Measures of Variability......Page 45
Supplementary Exercises: (73–96)......Page 56
2.1 Sample Spaces and Events......Page 62
2.2 Axioms, Interpretations, and Properties of Probability......Page 68
2.3 Counting Methods......Page 79
2.4 Conditional Probability......Page 88
2.5 Independence......Page 100
2.6 Simulation of Random Events......Page 107
Supplementary Exercises: (113–140)......Page 116
3.1 Random Variables......Page 123
3.2 Probability Distributions for Discrete Random Variables......Page 127
3.3 Expected Values of Discrete Random Variables......Page 138
3.4 Moments and Moment Generating Functions......Page 149
3.5 The Binomial Probability Distribution......Page 156
3.6 The Poisson Probability Distribution......Page 168
3.7 Other Discrete Distributions......Page 176
3.8 Simulation of Discrete Random Variables......Page 185
Supplementary Exercises: (138–169)......Page 194
4.1 Probability Density Functions and Cumulative Distribution Functions......Page 201
4.2 Expected Values and Moment Generating Functions......Page 215
4.3 The Normal Distribution......Page 225
4.4 The Gamma Distribution and Its Relatives......Page 242
4.5 Other Continuous Distributions......Page 251
4.6 Probability Plots......Page 259
4.7 Transformations of a Random Variable......Page 270
4.8 Simulation of Continuous Random Variables......Page 275
Supplementary Exercises: (131–159)......Page 281
5 Joint Probability Distributions and Their Applications......Page 288
5.2 Expected Values, Covariance, and Correlation......Page 305
5.3 Linear Combinations......Page 314
5.4 Conditional Distributions and Conditional Expectation......Page 328
5.5 The Bivariate Normal Distribution......Page 341
5.6 Transformations of Multiple Random Variables......Page 347
5.7 Order Statistics......Page 353
Supplementary Exercises: (122–150)......Page 361
6.1 Statistics and Their Distributions......Page 368
6.2 The Distribution of Sample Totals, Means, and Proportions......Page 379
6.3 The χ2, t, and F Distributions......Page 391
6.4 Distributions Based on Normal Random Samples......Page 399
Supplementary Exercises: (59–68)......Page 404
Appendix: Proof of the Central Limit Theorem......Page 406
7.1 Concepts and Criteria for Point Estimation......Page 408
7.2 The Methods of Moments and Maximum Likelihood......Page 427
7.3 Sufficiency......Page 439
7.4 Information and Efficiency......Page 447
Supplementary Exercises: (61–78)......Page 456
8 Statistical Intervals Based on a Single Sample......Page 461
8.1 Basic Properties of Confidence Intervals......Page 462
8.2 The One-Sample t Interval and Its Relatives......Page 473
8.3 Intervals for a Population Proportion......Page 485
8.4 Confidence Intervals for the Population Variance and Standard Deviation......Page 491
8.5 Bootstrap Confidence Intervals......Page 494
Supplementary Exercises (71–92)......Page 504
9.1 Hypotheses and Test Procedures......Page 510
9.2 Tests About a Population Mean......Page 521
9.3 Tests About a Population Proportion......Page 535
9.4 P-Values......Page 541
9.5 The Neyman–Pearson Lemma and Likelihood Ratio Tests......Page 551
9.6 Further Aspects of Hypothesis Testing......Page 562
Supplementary Exercises: (83–102)......Page 569
10.1 The Two-Sample z Confidence Interval and Test......Page 573
10.2 The Two-Sample t Confidence Interval and Test......Page 583
10.3 Analysis of Paired Data......Page 599
10.4 Inferences About Two Population Proportions......Page 610
10.5 Inferences About Two Population Variances......Page 619
10.6 Inferences Using the Bootstrap and Permutation Methods......Page 625
Supplementary Exercises: (95–124)......Page 638
11 The Analysis of Variance......Page 646
11.1 Single-Factor ANOVA......Page 647
11.2 Multiple Comparisons in ANOVA......Page 660
11.3 More on Single-Factor ANOVA......Page 669
11.4 Two-Factor ANOVA without Replication......Page 679
11.5 Two-Factor ANOVA with Replication......Page 694
Supplementary Exercises: (74–84)......Page 706
12 Regression and Correlation......Page 710
12.1 The Simple Linear Regression Model......Page 711
12.2 Estimating Model Parameters......Page 720
12.3 Inferences About the Regression Coefficient β1......Page 734
12.4 Inferences for the (Mean) Response......Page 744
12.5 Correlation......Page 752
12.6 Investigating Model Adequacy: Residual Analysis......Page 764
12.7 Multiple Regression Analysis......Page 774
12.8 Quadratic, Interaction, and Indicator Terms......Page 790
12.9 Regression with Matrices......Page 802
12.10 Logistic Regression......Page 813
Supplementary Exercises: (121–138)......Page 824
13.1 Goodness-of-Fit Tests......Page 830
13.2 Two-Way Contingency Tables......Page 847
Supplementary Exercises: (32–43)......Page 858
14.1 Exact Inference for Population Quantiles......Page 862
14.2 One-Sample Rank-Based Inference......Page 868
14.3 Two-Sample Rank-Based Inference......Page 878
14.4 Nonparametric ANOVA......Page 886
Supplementary Exercises: (49–58)......Page 893
15.1 Prior and Posterior Distributions......Page 896
15.2 Bayesian Point and Interval Estimation......Page 903
Appendix_1......Page 909
Appendix_2......Page 932
Bib1......Page 968
Index......Page 970