| Description |
1 online resource |
| Series |
Wiley series in probability and statistics |
|
Wiley series in probability and statistics
|
| Contents |
Experiments, Sample Spaces, and Events -- Probability -- Counting -- Conditional Probability, Independence, and Markov Chains -- Random Variables: Univariate Case -- Random Variables: Multivariate Case -- Expectation -- Selected Families of Distributions -- Random Samples -- Introduction to Statistical Inference -- Estimation -- Testing Statistical Hypotheses -- Linear Models -- Rank Methods -- Analysis of Categorical Data -- Basics of Bayesian Statistics -- Supporting R Code -- Statistical Tables -- Bibliography -- Answers to Odd-Numbered Problems |
|
Preface vii; Preface vi; 1 Experiments, Sample Spaces, and Events 1; 1.1 Introduction 1; 1.2 Sample Space 2; 1.3 Algebra of Events 9; 1.4 Infinite Operations on Events 15; 2 Probability 25; 2.1 Introduction 25; 2.2 Probability as a Frequency 25; 2.3 Axioms of Probability 26; 2.4 Consequences of the Axioms 31; 2.5 Classical Probability 35; 2.6 Necessity of the Axioms* 36; 2.7 Subjective Probability* 41; 3 Counting 45; 3.1 Introduction 45; 3.2 Product Sets, Orderings, and Permutations 45; 3.3 Binomial Coefficients 51; 3.4 Multinomial Coefficients 64; 4 Conditional Probability, Independence, and Markov Chains 67; 4.1 Introduction 67; 4.2 Conditional Probability 68; 4.3 Partitions; Total Probability Formula 74; 4.4 Bayes' Formula 79; 4.5 Independence 84; 4.6 Exchangeability; Conditional Independence 90; 4.7 Markov Chains* 93; 5 Random Variables: Univariate Case 107; 5.1 Introduction 107; 5.2 Distributions of Random Variables 108; 5.3 Discrete and Continuous Random Variables 117; 5.4 Functions of Random Variables 129; 5.5 Survival and Hazard Functions 136; 6 Random Variables: Multivariate Case 141; 6.1 Bivariate Distributions 141; 6.2 Marginal Distributions; Independence 148; 6.3 Conditional Distributions 160; 6.4 Bivariate Transformations 167; 6.5 Multidimensional Distributions 176; 7 Expectation 183; 7.1 Introduction 183; 7.2 Expected Value 184; 7.3 Expectation as an Integral* 192; 7.4 Properties of Expectation 199; 7.5 Moments 207; 7.6 Variance 215; 7.7 Conditional Expectation 227; 7.8 Inequalities 231; 8 Selected Families of Distributions 237; 8.1 Bernoulli Trials and Related Distributions 237; 8.2 Hypergeometric Distribution 251; 8.3 Poisson Distribution and Poisson Process 256; 8.4 Exponential, Gamma and Related Distributions 269; 8.5 Normal Distribution 276; 8.6 Beta Distribution 286; 9 Random Samples 293; 9.1 Statistics and Sampling Distributions 293; 9.2 Distributions Related to Normal 295; 9.3 Order Statistics 300; 9.4 Generating Random Samples 307; 9.5 Convergence 312; 9.6 Central Limit Theorem 322; 10 Introduction to Statistical Inference 331; 10.1 Overview 331; 10.2 Basic Models 334; 10.3 Sampling 336; 10.4 Measurement Scales 342; 11 Estimation 347; 11.1 Introduction 347; 11.2 Consistency 352; 11.3 Loss, Risk, and Admissibility 355; 11.4 Efficiency 361; 11.5 Methods of Obtaining Estimators 368; 11.6 Sufficiency 387; 11.7 Interval Estimation 403; 12 Testing Statistical Hypotheses 419; 12.1 Introduction 419; 12.2 Intuitive Background 423; 12.3 Most Powerful Tests 432; 12.4 Uniformly Most Powerful Tests 445; 12.5 Unbiased Tests 452; 12.6 Generalized Likelihood Ratio Tests 456; 12.7 Conditional Tests 463; 12.8 Tests and Confidence Intervals 466; 12.9 Review of Tests for Normal Distributions 467; 12.10 Monte Carlo, Bootstrap, and Permutation Tests 477; 14 Linear Models 483; 14.1 Introduction 483; 14.2 Regression of the First and Second Kind 485; 14.3 Distributional Assumptions 491; 14.4 Linear Regression in the Normal Case 494; 14.5 Testing Linearity 500; 14.6 Prediction 503; 14.7 Inverse Regression 505; 14.8 BLUE 508; 14.9 Regression Toward the Mean 510; 14.10 Analysis of Variance 512; 14.11 One-Way Layout 512; 14.12 Two-Way Layout 516; 14.13 ANOVA Models with Interaction 518; 14.14 Further Extensions 522; 15 Rank Methods 525; 15.1 Introduction 525; 15.2 Glivenko-Cantelli Theorem 526; 15.3 Kolmogorov-Smirnov Tests 530; 15.4 One-Sample Rank Tests 537; 15.5 Two-Sample Rank Tests 544; 15.6 Kruskal-Wallis Test 548; 16 Analysis of Categorical Data 551; 16.1 Introduction 551; 16.2 Chi-Square Tests 553; 16.3 Homogeneity and Independence 559; 16.4 Consistency and Power 565; 16.5 2×2 Contingency Tables 570; 16.6 r × c Contingency Tables 578; 17 Basics of Bayesian Statistics 583; 17.1 Introduction 583; 17.2 Prior and Posterior Distributions 584; 17.3 Bayesian Inference 592; 17.4 Final Comments 608; Appendix 1 609; Appendix 2 616; Bibliography 619; Answers to Odd-Numbered Problems 624; Index 632; Index 632 |
| Summary |
"Probability and Statistical Inference, Third Edition is a user-friendly book that stresses the comprehension of concepts instead of the simple acquisition of a skill or tool. It provides a mathematical framework that permits students to carry out various procedures using R. Its unique approach to problems allows readers to integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic. The book focuses on the development of intuition and understanding through diversity of experience. New to this edition, in addition to R code, are a chapter on Bayesian statistics, additional concepts introduced, and new and improved problems and mini-projects. The book is intended for upper-level undergraduates or first year graduate students in the in statistics or related disciplines such as mathematics or engineering, where exposure to statistics is needed"-- Provided by publisher |
| Notes |
Revised edition of: Probability and statistical inference / Robert Bartoszyński, Magdalena Niewiadomska-Bugaj. 2nd ed. c2008 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on print version record and CIP data provided by publisher; resource not viewed |
| Subject |
Probabilities.
|
|
Mathematical statistics.
|
|
probability.
|
|
Mathematical statistics
|
|
Probabilities
|
| Form |
Electronic book
|
| Author |
Bartoszyński, Robert, author
|
| LC no. |
2020021072 |
| ISBN |
9781119243830 |
|
1119243831 |
|
9781119243823 |
|
1119243823 |
|
9781119243816 |
|
1119243815 |
|
