Natural Introduction to Probability Theory

ISBN-10: 3764387238
ISBN-13: 9783764387235
Edition: 2nd 2008
Authors: Ronald Meester
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Description: 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  More...

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Book details

Edition: 2nd
Copyright year: 2008
Publisher: Birkhauser Verlag GmbH
Publication date: 2/18/2008
Binding: Paperback
Pages: 198
Size: 10.00" wide x 6.75" long x 1.00" tall
Weight: 1.144

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.

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

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