Probability and Statistical Inference. Robert Bartoszynski
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Table of Contents
1 Cover
2 Wiley Series in Probability and Statistics
3 Probability and Statistical Inference
9 Chapter 1: Experiments, Sample Spaces, and Events 1.1 Introduction 1.2 Sample Space 1.3 Algebra of Events 1.4 Infinite Operations on Events Notes
10 Chapter 2: Probability 2.1 Introduction 2.2 Probability as a Frequency 2.3 Axioms of Probability 2.4 Consequences of the Axioms 2.5 Classical Probability 2.6 Necessity of the Axioms* 2.7 Subjective Probability* Note
11 Chapter 3: Counting 3.1 Introduction 3.2 Product Sets, Orderings, and Permutations 3.3 Binomial Coefficients 3.4 Multinomial Coefficients Notes
12 Chapter 4: Conditional Probability, Independence, and Markov Chains 4.1 Introduction 4.2 Conditional Probability 4.3 Partitions; Total Probability Formula 4.4 Bayes' Formula 4.5 Independence 4.6 Exchangeability; Conditional Independence 4.7 Markov Chains* Note
13 Chapter 5: Random Variables: Univariate Case 5.1 Introduction 5.2 Distributions of Random Variables 5.3 Discrete and Continuous Random Variables 5.4 Functions of Random Variables 5.5 Survival and Hazard Functions Notes
14 Chapter 6: Random Variables: Multivariate Case 6.1 Bivariate Distributions 6.2 Marginal Distributions; Independence 6.3 Conditional Distributions 6.4 Bivariate Transformations 6.5 Multidimensional Distributions
15 Chapter 7: Expectation 7.1 Introduction 7.2 Expected Value 7.3 Expectation as an Integral* 7.4 Properties of Expectation 7.5 Moments 7.6 Variance 7.7 Conditional Expectation 7.8 Inequalities
16 Chapter 8: Selected Families of Distributions 8.1 Bernoulli Trials and Related Distributions 8.2 Hypergeometric Distribution 8.3 Poisson Distribution and Poisson Process 8.4 Exponential, Gamma, and Related Distributions 8.5 Normal Distribution 8.6 Beta Distribution Notes
17 Chapter 9: Random Samples 9.1 Statistics and Sampling Distributions 9.2 Distributions Related to Normal 9.3 Order Statistics 9.4 Generating Random Samples 9.5 Convergence