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 Statisti...

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Hauptverfasser:	Niewiadomska-Bugaj, Magdalena 20./21. Jh (VerfasserIn), Bartoszyński, Robert 1933-1998 (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Hoboken, NJ Wiley-Interscience 2020
Ausgabe:	Third edition
Schriftenreihe:	Wiley series in probability and statistics
Schlagworte:	Statistik Wahrscheinlichkeitsrechnung Statistische Schlussweise Probabilities Mathematical statistics
Online-Zugang:	UBY01 Volltext
Zusammenfassung:	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
Beschreibung:	Revised edition of: Probability and statistical inference / Robert Bartoszyński, Magdalena Niewiadomska-Bugaj. 2nd ed. c2008 Includes bibliographical references and index 2010
Beschreibung:	1 Online-Ressource
ISBN:	9781119243830 1119243831 9781119243823 1119243823 9781119243816 1119243815
DOI:	10.1002/9781119243830