UID:
almafu_9959835949702883
Format:
1 online resource
Edition:
Third edition.
ISBN:
9781119243830
,
1119243831
,
9781119243823
,
1119243823
,
9781119243816
,
1119243815
Series Statement:
Wiley series in probability and statistics
Content:
"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"--
Note:
Revised edition of: Probability and statistical inference / Robert Bartoszyński, Magdalena Niewiadomska-Bugaj. 2nd ed. c2008.
,
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.
,
〈P〉Preface vii〈/p〉 〈p〉Preface vi〈/p〉 〈p〉1 Experiments, Sample Spaces, and Events 1〈/p〉 〈p〉1.1 Introduction 1〈/p〉 〈p〉1.2 Sample Space 2〈/p〉 〈p〉1.3 Algebra of Events 9〈/p〉 〈p〉1.4 Infinite Operations on Events 15〈/p〉 〈p〉2 Probability 25〈/p〉 〈p〉2.1 Introduction 25〈/p〉 〈p〉2.2 Probability as a Frequency 25〈/p〉 〈p〉2.3 Axioms of Probability 26〈/p〉 〈p〉2.4 Consequences of the Axioms 31〈/p〉 〈p〉2.5 Classical Probability 35〈/p〉 〈p〉2.6 Necessity of the Axioms* 36〈/p〉 〈p〉2.7 Subjective Probability* 41〈/p〉 〈p〉3 Counting 45〈/p〉 〈p〉3.1 Introduction 45〈/p〉 〈p〉3.2 Product Sets, Orderings, and Permutations 45〈/p〉 〈p〉3.3 Binomial Coefficients 51〈/p〉 〈p〉3.4 Multinomial Coefficients 64〈/p〉 〈p〉4 Conditional Probability, Independence, and Markov Chains 67〈/p〉 〈p〉4.1 Introduction 67〈/p〉 〈p〉4.2 Conditional Probability 68〈/p〉 〈p〉4.3 Partitions; Total Probability Formula 74〈/p〉 〈p〉4.4 Bayes' Formula 79〈/p〉 〈p〉4.5 Independence 84〈/p〉 〈p〉4.6 Exchangeability; Conditional Independence 90〈/p〉 〈p〉4.7 Markov Chains* 93〈/p〉 〈p〉5 Random Variables: Univariate Case 107〈/p〉 〈p〉5.1 Introduction 107〈/p〉 〈p〉5.2 Distributions of Random Variables 108〈/p〉 〈p〉5.3 Discrete and Continuous Random Variables 117〈/p〉 〈p〉5.4 Functions of Random Variables 129〈/p〉 〈p〉5.5 Survival and Hazard Functions 136〈/p〉 〈p〉6 Random Variables: Multivariate Case 141〈/p〉 〈p〉6.1 Bivariate Distributions 141〈/p〉 〈p〉6.2 Marginal Distributions; Independence 148〈/p〉 〈p〉6.3 Conditional Distributions 160〈/p〉 〈p〉6.4 Bivariate Transformations 167〈/p〉 〈p〉6.5 Multidimensional Distributions 176〈/p〉 〈p〉7 Expectation 183〈/p〉 〈p〉7.1 Introduction 183〈/p〉 〈p〉7.2 Expected Value 184〈/p〉 〈p〉7.3 Expectation as an Integral* 192〈/p〉 〈p〉7.4 Properties of Expectation 199〈/p〉 〈p〉7.5 Moments 207〈/p〉 〈p〉7.6 Variance 215〈/p〉 〈p〉7.7 Conditional Expectation 227〈/p〉 〈p〉7.8 Inequalities 231〈/p〉 〈p〉8 Selected Families of Distributions 237〈/p〉 〈p〉8.1 Bernoulli Trials and Related Distributions 237〈/p〉 〈p〉8.2 Hypergeometric Distribution 251〈/p〉 〈p〉8.3 Poisson Distribution and Poisson Process 256〈/p〉 〈p〉8.4 Exponential, Gamma and Related Distributions 269〈/p〉 〈p〉8.5 Normal Distribution 276〈/p〉 〈p〉8.6 Beta Distribution 286〈/p〉 〈p〉9 Random Samples 293〈/p〉 〈p〉9.1 Statistics and Sampling Distributions 293〈/p〉 〈p〉9.2 Distributions Related to Normal 295〈/p〉 〈p〉9.3 Order Statistics 300〈/p〉 〈p〉9.4 Generating Random Samples 307〈/p〉 〈p〉9.5 Convergence 312〈/p〉 〈p〉9.6 Central Limit Theorem 322〈/p〉 〈p〉10 Introduction to Statistical Inference 331〈/p〉 〈p〉10.1 Overview 331〈/p〉 〈p〉10.2 Basic Models 334〈/p〉 〈p〉10.3 Sampling 336〈/p〉 〈p〉10.4 Measurement Scales 342〈/p〉 〈p〉11 Estimation 347〈/p〉 〈p〉11.1 Introduction 347〈/p〉 〈p〉11.2 Consistency 352〈/p〉 〈p〉11.3 Loss, Risk, and Admissibility 355〈/p〉 〈p〉11.4 Efficiency 361〈/p〉 〈p〉11.5 Methods of Obtaining Estimators 368〈/p〉 〈p〉11.6 Sufficiency 387〈/p〉 〈p〉11.7 Interval Estimation 403〈/p〉 〈p〉12 Testing Statistical Hypotheses 419〈/p〉 〈p〉12.1 Introduction 419〈/p〉 〈p〉12.2 Intuitive Background 423〈/p〉 〈p〉12.3 Most Powerful Tests 432〈/p〉 〈p〉12.4 Uniformly Most Powerful Tests 445〈/p〉 〈p〉12.5 Unbiased Tests 452〈/p〉 〈p〉12.6 Generalized Likelihood Ratio Tests 456〈/p〉 〈p〉12.7 Conditional Tests 463〈/p〉 〈p〉12.8 Tests and Confidence Intervals 466〈/p〉 〈p〉12.9 Review of Tests for Normal Distributions 467〈/p〉 〈p〉12.10 Monte Carlo, Bootstrap, and Permutation Tests 477〈/p〉 〈p〉14 Linear Models 483〈/p〉 〈p〉14.1 Introduction 483〈/p〉 〈p〉14.2 Regression of the First and Second Kind 485〈/p〉 〈p〉14.3 Distributional Assumptions 491〈/p〉 〈p〉14.4 Linear Regression in the Normal Case 494〈/p〉 〈p〉14.5 Testing Linearity 500〈/p〉 〈p〉14.6 Prediction 503〈/p〉 〈p〉14.7 Inverse Regression 505〈/p〉 〈p〉14.8 BLUE 508〈/p〉 〈p〉14.9 Regression Toward the Mean 510〈/p〉 〈p〉14.10 Analysis of Variance 512〈/p〉 〈p〉14.11 One-Way Layout 512〈/p〉 〈p〉14.12 Two-Way Layout 516〈/p〉 〈p〉14.13 ANOVA Models with Interaction 518〈/p〉 〈p〉14.14 Further Extensions 522〈/p〉 〈p〉15 Rank Methods 525〈/p〉 〈p〉15.1 Introduction 525〈/p〉 〈p〉15.2 Glivenko-Cantelli Theorem 526〈/p〉 〈p〉15.3 Kolmogorov-Smirnov Tests 530〈/p〉 〈p〉15.4 One-Sample Rank Tests 537〈/p〉 〈p〉15.5 Two-Sample Rank Tests 544〈/p〉 〈p〉15.6 Kruskal-Wallis Test 548〈/p〉 〈p〉16 Analysis of Categorical Data 551〈/p〉 〈p〉16.1 Introduction 551〈/p〉 〈p〉16.2 Chi-Square Tests 553〈/p〉 〈p〉16.3 Homogeneity and Independence 559〈/p〉 〈p〉16.4 Consistency and Power 565〈/p〉 〈p〉16.5 2×2 Contingency Tables 570〈/p〉 〈p〉16.6 r × c Contingency Tables 578〈/p〉 〈p〉17 Basics of Bayesian Statistics 583〈/p〉 〈p〉17.1 Introduction 583〈/p〉 〈p〉17.2 Prior and Posterior Distributions 584〈/p〉 〈p〉17.3 Bayesian Inference 592〈/p〉 〈p〉17.4 Final Comments 608〈/p〉 〈p〉Appendix 1 609〈/p〉 〈p〉Appendix 2 616〈/p〉 〈p〉Bibliography 619〈/p〉 〈p〉Answers to Odd-Numbered Problems 624〈/p〉 〈p〉Index 632〈/p〉 〈p〉Index 632〈/p〉
Additional Edition:
Print version: Niewiadomska-Bugaj, Magdalena. Probability and statistical inference Hoboken, NJ : Wiley-Interscience, 2020. ISBN 9781119243809
Language:
English
Keywords:
Electronic books.
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Electronic books.
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Electronic books.
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119243830
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119243830
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119243830
