A natural introduction to probability theory
By: Ronald Meester.
Edition: First edition
Publisher: Birkhauser·
Published: 2003
Place of publication: Basel
Language: eng
Number of pages: 191
Table of contents: title: .; title: Contents    vi; title: Intermezzo 83; title: LI Uncountable Sample Spaces 83; title: 1.2 An Event Without a Probability?! 84; title: 1.3 Random Variables on Uncountable Sample Spaces 86; title: 5 Continuous Random Variables and Vectors 87; title: 5.1 Experiments 87; title: 5.2 Properties of Probability Measures 92; title: 5.3 Continuous Random Variables 94; title: 5.4 Expectation 99; title: 5.5 Random Vectors and Independence 103; title: 5.6 Functions of Random Variables and Vectors 107; title: 5.7 Sums of Random Variables Ill; title: 5.8 More About the Expectation; Variance 112; title: 5.9 Random Variables Which are Neither Discrete Nor Continuous . . 116; title: 5.10 Conditional Distributions and Expectations 118; title: 5.11 The Law of Large Numbers 124; title: 5.12 Exercises 125; title: 6 Infinitely Many Repetitions 131; title: 6.1 Infinitely Many Coin Flips and Random Points in (0, 1] 132; title: 6.2 A More General Approach to Infinitely Many Repetitions 134; title: 6.3 The Strong Law of Large Numbers 136; title: 6.4 Random Walk Revisited 141; title: 6.5 Branching Processes 141; title: 6.6 Exercises 145; title: 7 The Poisson Process 147; title: 7.1 Building a Model 147; title: 7.2 Basic Properties 152; title: 7.3 The Waiting Time Paradox 156; title: 7.4 The Strong Law of Large Numbers 158; title: 7.5 Exercises 159; title: 8 Limit Theorems 161; title: 8.1 Weak Convergence 161; title: 8.2 Characteristic Functions 163; title: 8.3 Expansion of the Characteristic Function 168; title: 8.4 The Law of Large Numbers 170; title: 8.5 The Central Limit Theorem 173; title: 8.6 Exercises 175; title: 9 Extending the Probabilities 177; title: 9.1 General Probability Measures 177; title: Contents; title: A Interpreting Probabilities B Further Reading C Answers to Selected Exercises; title: Index; title: .