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1 Burnside Mathematics- Probability Theory

Probability Statistics & Truth 2ND Edition

by

Probability Statistics & Truth 2ND Edition Cover

 

Synopses & Reviews

Publisher Comments:

This comprehensive study of probability, its relation to statistics, and its truth-finding value considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics. Numerous examples complement the text.

Synopsis:

Classic, lucid treatment of probability theory, its relation to statistics, and its truth-finding value.

Synopsis:

This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.

Table of Contents

PREFACE

PREFACE TO THE THIRD GERMAN EDITION

FIRST LECTURE The Definition of Probability

  Amendment of Popular Terminology

  Explanation of Words

  Synthetic Definitions

  Terminology

  The Concept of Work in Mechanics

  An Historical Interlude

  The Purpose of Rational Concepts

  The Inadequacy of Theories

  Limitation of Scope

  Unlimited Repetition

  The Collective

  The First Step towards a Definition

  Two Different Pairs of Dice

  Limiting Value of Relative Frequency

  The Experimental Basis of the Theory of Games

  The Probability of Death

  First the Collective-then the Probability

  Probability in the Gas Theory

  An Historical Remark

  Randomness

  Definition of Randomness: Place Selection

  The Principle of the Impossibility of a Gambling System

  Example of Randomness

  Summary of the Definition

SECOND LECTURE The Elements of the Theory of Probability

  The Theory of Probability is a Science Similar to Others

  The Purpose of the Theory of Probability

  The Beginning and the End of Each Problem must be Probabilities

  Distribution in a Collective

  Probability of a Hit; Continuous Distribution

  Probability Density

  The Four Fundamental Operations

  First Fundamental Operation: Selection

  Second Fundamental Operation: Mixing

  Inexact Statement of the Addition Rule

  Uniform Distribution

  Summary of the Mixing Rule

  Third Fundamental Operation: Partition

  Probabilities after Partition

  Initial and Final Probability of an Attribute

  The So-called Probability of Causes

  Formulation of the rule of Partition

  Fourth Fundamental Operation: Combination

  A New Method of Forming Partial Sequences: Correlated Sampling

  Mutually Independent Collectives

  Derivation of the Multiplication Rule

  Test of Independence

  Combination of Dependent Collectives

  Example of Noncombinable Collectives

  Summary of the Four Fundamental Operations

  A Problem of Chevalier de Méré

  Solution of the Problem of Chevalier de Méré

  Discussion of the Solution

  Some Final Conclusions

  Short Review

THIRD LECTURE Critical Discussion of the Foundations of Probability

  The Classical Definition of Probability

  Equally Likely Cases ...

  ... Do Not Always Exist

  A Geometrical Analogy

  How to Recognize Equally Likely Cases

  Are Equally Likely Cases of Exceptional Significance?

  The Subjective Conception of Probability

  Bertrand's Paradox

  The Suggested Link between the Classical and the New Definitions of Probability

  Summary of Objections to the Classical Definition

  Objections to My Theory

  Finite Collectives

  Testing Probability Statements

  An Objection to the First Postulate

  Objections to the Condition of Randomness

  Restricted Randomness

  Meaning of the Condition of Randomness

  Consistency of the Randomness Axiom

  A Problem of Terminology

  Objections to the Frequency Concept

  Theory of the Plausibility of Statements

  The Nihilists

  Restriction to One Single Initial Collective

  Probability as Part of the Theory of Sets

  Development of the Frequency Theory

  Summary and Conclusion

FOURTH LECTURE The Laws of Large Numbers

  Poisson's Two Different Propositions

  Equally Likely Events

  Arithmetical Explanation

  Subsequent Frequency Definition

  The Content of Poisson's Theorem

  Example of a Sequence to which Poisson's Theorem does not Apply

  Bernoulli and non-Bernoulli Sequences

  Derivation of the Bernoulli-Poison Theorem

  Summary

  Inference

  Bayes's Problem

  Initial and Inferred Probability

  Longer Sequences of Trials

  Independence of the Initial Distribution

  The Relation of Bayes's Theorem to Poisson's Theorem

  The Three Propositions

  Generalization of the Laws of Large Numbers

  The Strong Law of Large Numbers

  The Statistical Functions

  The First Law of Large Numbers for Statistical Functions

  The Second Law of Large Numbers for Statistical Functions

  Closing Remarks

FIFTH LECTURE Application Statistics and the Theory of Errors

  What is Statistics?

  Games of Chance and Games of Skill

  Marbe's Uniformity in the World'

  Answer to Marbe's Problem

  Theory of Accumulation and the Law of Series

  Linked Events

  The General Purpose of Statistics

  Lexis' Theory of Dispersion

  The Mean and the Dispersion

  Comparison between the Observed and the Expected Variance

  Lexis' Theory and the Laws of Large Numbers

  Normal and Nonnormal Dispersion

  Sex Distribution of Infants

  Statistics of Deaths with Supernormal Dispersion

  Solidarity of Cases

  Testing Hypotheses

  R. A. Fisher's Likelihood'

  Small Sample Theory

  Social and Biological Statistics

  Mendel's Theory of Heredity

  Industrial and Technological Statistics

  An Example of Faulty Statistics

  Correction

  Some Results Summarized

  Descriptive Statistics

  Foundations of the Theory of Errors

  Galton's Board

  Normal Curve

  Laplace's Law

  The Application of the Theory of Errors

SIXTH LECTURE Statistical Problems in Physics

  The Second Law of Thermodynamics

  Determinism and Probability

  Chance Mechanisms

  Random Fluctuations

  Small Causes and Large Effects

  Kinetic Theory of Gases

  Order of Magnitude of 'Improbability'

  Criticism of the Gas Theory

  Brownian Motion

  Evolution of Phenomena in Time

  Probability 'After Effects'

  Residence Time and Its Prediction

  Entropy Theorem and Markoff Chains

  Svedberg's Experiments

  Radioactivity

  Prediction of Time Intervals

  Marsden's and Barratt's Experiments

  Recent Development in the Theory of Gases

  Degeneration of Gases: Electron Theory of Metals

  Quantum Theory

  Statistics and Causality

  Causal Explanation Newton's Sense

  Limitations of Newtonian Mechanics

  Simplicity as a Criterion of Causality

  Giving up the Concept of Causality

  The Law of Causality

  New Quantum Statistics

  Are Exact Measurements Possible?

  Position and Velocity of a Material Particle

  Heisenberg's Uncertainty Principle

  Consequences for our Physical Concept of the World

  Final Considerations

SUMMARY OF THE SIX LECTURES IN SIXTEEN PROPOSITIONS

NOTES AND ADDENDA

SUBJECT INDEX

NAME INDEX

Product Details

ISBN:
9780486242149
Translator:
Geiringer, Hilda
Author:
Geiringer, Hilda
Author:
Von
Author:
Von Mises, Richard
Author:
Mises, Richard Von
Author:
Mises, Richard
Publisher:
Dover Publications
Location:
New York :
Subject:
General
Subject:
General science
Subject:
Mathematics
Subject:
Statistics
Subject:
Probability
Subject:
Probabilities
Subject:
Probability & Statistics - General
Subject:
General Science
Subject:
Mathematics | Probability and Statistics
Copyright:
Edition Number:
2
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
Tome XXI, No. 8
Publication Date:
19810931
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
244
Dimensions:
8.5 x 5.38 in 0.63 lb

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Probability Statistics & Truth 2ND Edition Used Trade Paper
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Product details 244 pages Dover Publications - English 9780486242149 Reviews:
"Synopsis" by , Classic, lucid treatment of probability theory, its relation to statistics, and its truth-finding value.

"Synopsis" by ,
This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.
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