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E-raamat: Probability and Statistical Inference

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(The Ohio State University), (West Virginia University)
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Updated classic statistics text, with new problems and examples

Probability and Statistical Inference, Third Edition helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material.

In this Third Edition, the reader will find a new chapter on Bayesian statistics, 70 new problems and an appendix with the supporting R code. This book is suitable for upper-level undergraduates or first-year graduate students studying statistics or related disciplines, such as mathematics or engineering. This Third Edition:





Introduces an all-new chapter on Bayesian statistics and offers thorough explanations of advanced statistics and probability topics Includes 650 problems and over 400 examples - an excellent resource for the mathematical statistics class sequence in the increasingly popular "flipped classroom" format Offers students in statistics, mathematics, engineering and related fields a user-friendly resource Provides practicing professionals valuable insight into statistical tools

Probability and Statistical Inference offers a unique approach to problems that allows the reader to fully integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.
Preface to Third Edition xi
Preface to Second Edition xiii
About the Companion Website xvi
1 Experiments, Sample Spaces, and Events
1(20)
1.1 Introduction
1(1)
1.2 Sample Space
2(6)
1.3 Algebra of Events
8(5)
1.4 Infinite Operations on Events
13(8)
2 Probability
21(18)
2.1 Introduction
21(1)
2.2 Probability as a Frequency
21(1)
2.3 Axioms of Probability
22(4)
2.4 Consequences of the Axioms
26(4)
2.5 Classical Probability
30(1)
2.6 Necessity of the Axioms
31(4)
2.7 Subjective Probability
35(4)
3 Counting
39(20)
3.1 Introduction
39(1)
3.2 Product Sets, Orderings, and Permutations
39(5)
3.3 Binomial Coefficients
44(12)
3.4 Multinomial Coefficients
56(3)
4 Conditional Probability, Independence, and Markov Chains
59(34)
4.1 Introduction
59(1)
4.2 Conditional Probability
60(5)
4.3 Partitions; Total Probability Formula
65(4)
4.4 Bayes' Formula
69(5)
4.5 Independence
74(6)
4.6 Exchangeability; Conditional Independence
80(2)
4.7 Markov Chains*
82(11)
5 Random Variables: Univariate Case
93(30)
5.1 Introduction
93(1)
5.2 Distributions of Random Variables
94(8)
5.3 Discrete and Continuous Random Variables
102(10)
5.4 Functions of Random Variables
112(6)
5.5 Survival and Hazard Functions
118(5)
6 Random Variables: Multivariate Case
123(40)
6.1 Bivariate Distributions
123(6)
6.2 Marginal Distributions; Independence
129(11)
6.3 Conditional Distributions
140(7)
6.4 Bivariate Transformations
147(8)
6.5 Multidimensional Distributions
155(8)
7 Expectation
163(48)
7.1 Introduction
163(1)
7.2 Expected Value
164(7)
7.3 Expectation as an Integral
171(6)
7.4 Properties of Expectation
177(7)
7.5 Moments
184(7)
7.6 Variance
191(11)
7.7 Conditional Expectation
202(4)
7.8 Inequalities
206(5)
8 Selected Families of Distributions
211(48)
8.1 Bernoulli Trials and Related Distributions
211(12)
8.2 Hypergeometric Distribution
223(5)
8.3 Poisson Distribution and Poisson Process
228(12)
8.4 Exponential, Gamma, and Related Distributions
240(6)
8.5 Normal Distribution
246(9)
8.6 Beta Distribution
255(4)
9 Random Samples
259(36)
9.1 Statistics and Sampling Distributions
259(2)
9.2 Distributions Related to Normal
261(5)
9.3 Order Statistics
266(6)
9.4 Generating Random Samples
272(4)
9.5 Convergence
276(11)
9.6 Central Limit Theorem
287(8)
10 Introduction to Statistical Inference
295(14)
10.1 Overview
295(3)
10.2 Basic Models
298(1)
10.3 Sampling
299(6)
10.4 Measurement Scales
305(4)
11 Estimation
309(64)
11.1 Introduction
309(4)
11.2 Consistency
313(3)
11.3 Loss, Risk, and Admissibility
316(5)
11.4 Efficiency
321(7)
11.5 Methods of Obtaining Estimators
328(17)
11.6 Sufficiency
345(14)
11.7 Interval Estimation
359(14)
12 Testing Statistical Hypotheses
373(56)
12.1 Introduction
373(4)
12.2 Intuitive Background
377(7)
12.3 Most Powerful Tests
384(12)
12.4 Uniformly Most Powerful Tests
396(6)
12.5 Unbiased Tests
402(3)
12.6 Generalized Likelihood Ratio Tests
405(7)
12.7 Conditional Tests
412(3)
12.8 Tests and Confidence Intervals
415(1)
12.9 Review of Tests for Normal Distributions
416(8)
12.10 Monte Carlo, Bootstrap, and Permutation Tests
424(5)
13 Linear Models
429(38)
13.1 Introduction
429(2)
13.2 Regression of the First and Second Kind
431(5)
13.3 Distributional Assumptions
436(2)
13.4 Linear Regression in the Normal Case
438(6)
13.5 Testing Linearity
444(3)
13.6 Prediction
447(2)
13.7 Inverse Regression
449(2)
13.8 BLUE
451(2)
13.9 Regression Toward the Mean
453(2)
13.10 Analysis of Variance
455(1)
13.11 One-Way Layout
455(3)
13.12 Two-Way Layout
458(3)
13.13 ANOVA Models with Interaction
461(4)
13.14 Further Extensions
465(2)
14 Rank Methods
467(24)
14.1 Introduction
467(1)
14.2 Glivenko-Cantelli Theorem
468(3)
14.3 Kolmogorov-Smirnov Tests
471(7)
14.4 One-Sample Rank Tests
478(6)
14.5 Two-Sample Rank Tests
484(4)
14.6 Kruskal-Wallis Test
488(3)
15 Analysis of Categorical Data
491(30)
15.1 Introduction
491(1)
15.2 Chi-Square Tests
492(7)
15.3 Homogeneity and Independence
499(5)
15.4 Consistency and Power
504(5)
15.5 2 × 2 Contingency Tables
509(7)
15.6 R × c Contingency Tables
516(5)
16 Basics of Bayesian Statistics
521(24)
16.1 Introduction
521(1)
16.2 Prior and Posterior Distributions
522(7)
16.3 Bayesian Inference
529(14)
16.4 Final Comments
543(2)
Appendix A Supporting R Code 545(6)
Appendix B Statistical Tables 551(4)
Bibliography 555(4)
Answers to Odd-Numbered Problems 559(12)
Index 571
MAGDALENA NIEWIADOMSKA-BUGAJ, PHD, is Professor and Chair of the Statistics Department at Western Michigan University. Dr. Niewiadomska-Bugaj's areas of interest include general statistical methodology, nonparametric statistics, classification, and categorical data analysis. She has published over 50 papers, books, and book chapters in theoretical and applied statistics

The late ROBERT BARTOSZYSKI, PHD, was Professor in the Department of Statistics at The Ohio State University. His scientific contributions included research in the theory of stochastic processes and modeling biological phenomena. Throughout his career, Dr Bartoszyñski published books, book chapters, and over 100 journal articles.
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