Natural Introduction to Probability Theory

Name: Natural Introduction to Probability Theory
Availability: InStock
ISBN: 9783764387235

ISBN-10: 3764387238

ISBN-13: 9783764387235

Edition: 2nd 2008

Authors: Ronald Meester

List price: $54.99

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This introduction to probability theory is illustrated with many original examples and problems taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports and coding theory.

Book details

List price: $54.99
Edition: 2nd
Copyright year: 2008
Publisher: Springer Basel AG
Publication date: 2/18/2008
Binding: Paperback
Pages: 198
Size: 6.69" wide x 9.53" long x 1.00" tall
Weight: 0.924
Language: English



Preface to the First Edition


Preface to the Second Edition



Experiments



Definitions and Examples



Counting and Combinatorics



Properties of Probability Measures



Conditional Probabilities



Independence



A First Law of Large Numbers



Exercises



Random Variables and Random Vectors



Random Variables



Independence



Expectation and Variance



Random Vectors



Conditional Distributions and Expectations



Generating Functions



Exercises



Random Walk



Random Walk and Counting



The Arc-Sine Law



Exercises



Limit Theorems



The Law of Large Numbers



The Central Limit Theorem



Exercises


Intermezzo



Uncountable Sample Spaces



An Event Without a Probability?!



Random Variables on Uncountable Sample Spaces



Continuous Random Variables and Vectors



Experiments



Properties of Probability Measures



Continuous Random Variables



Expectation



Random Vectors and Independence



Functions of Random Variables and Vectors



Sums of Random Variables



More About the Expectation; Variance



Random Variables Which are Neither Discrete Nor Continuous



Conditional Distributions and Expectations



The Law of Large Numbers



Exercises



Infinitely Many Repetitions



Infinitely Many Coin Flips and Random Points in (0, 1]



A More General Approach to Infinitely Many Repetitions



The Strong Law of Large Numbers



Random Walk Revisited



Branching Processes



Exercises



The Poisson Process



Building a Model



Basic Properties



The Waiting Time Paradox



The Strong Law of Large Numbers



Exercises



Limit Theorems



Weak Convergence



Characteristic Functions



Expansion of the Characteristic Function



The Law of Large Numbers



The Central Limit Theorem



Exercises



Extending the Probabilities



General Probability Measures



Interpreting Probabilities



Further Reading



Answers to Selected Exercises


Index