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010			_a7289433
020			_a978-0045190010
040			_cFoundation University _bEnglish
082			_a004.422 M687
100			_aMises, Richard von _911210 _eauthor
245			_aProbability , Statistics and Truth / _cby Richard Von Mises
250			_aSECOND REVISED ENGLISH EDITION
260			_aLONDON. GEORGE ALLEN AND UNWIN LTD NEW YORK : _bTHE MACMILLAN COMPANY ; _c1957.
300			_aix, 243 pages : _billustrations ; _c22 cm.
504			_aIncludes bibliographical references and index.
505			_aCONTENTS PREFACE page V PREFACE TO THE THIRD GERMAN EDITION vii FIRST LECTURE The Definition of Probability Amendment of Popular Terminology 1 Explanation of Words 2 Synthetic Definitions 3 Terminology 4 The Concept of Work m Mechanics 5 An Historical Interlude 6 The Purpose of Rational Concepts 6 The Inadequacy of Theories 7 Limitation of Scope 8 Unlimited Repetition 10 The Collective 1 1 The First Step towards a Definition 12 Two Different Pairs of Dice 13 Limiting Value of Relative Frequency 14 The Experimental Basis of the Theory of Games 16 The Probability of Death 16 First the Collective — ^then the Probability 18 Probability in the Gas Theory 20 An Historical Remark 21 Randomness 23 Definition of Randomness: Place Selection 24 The Principle of the Impossibility of a Gambling System 25 Example of Randomness 27 Summary of the Definition 28 SECOND LECTURE The Elements of the Theory of Probability The Theory of Probability is a Science Similar to Others 30 The Purpose of the Theory of Probability 31 The Beginning and the End of Each Problem must be Probabilities 32 Distnbution in a Collective 34 Probability of a Hit; Continuous Distribution 35 Probability Density 36 The Four Fundamental Operations 38 First Fundamental Operation: Selection 39 CONTENTS Second Fundamental Operation: Mixing 39 Inexact Statement of the Addition Rule 40 Uniform Distribution 41 Summary of the Mixing Rule 43 Third Fundamental Operation: Partition 43 Probabihties after Partition 45 Initial and Final Probability of an Attribute 46 The So-called Probabihty of Causes 46 Formulation of the Rule of Partition 47 Fourth Fundamental Operation* Combination 48 A New Method of Forming Partial Sequences : Correlated Sampling 49 Mutually Independent Collectives 50 Derivation of the Multiplication Rule 51 Test of Independence 53 Combination of Dependent Collectives 55 Example of Noncombinable Collectives 56 Summary of the Four Fundamental Operations 57 A Problem of Chevalier de M6r6 58 Solution of the Problem of Chevalier de Mere 59 Discussion of the Solution 62 Some Final Conclusions 63 Short Review 64 THIRD LECTURE Critical Discussion of the Foundations of Probability The Classical Definition of Probability 66 Equally Likely Cases ... 68 ... Do Not Always Exist 69 A Geometrical Analogy 70 How to Recognize Equally Likely Cases 71 Are Equally Likely Cases of Exceptional Significance? 73 The Subjective Conception of Probability 75 Bertrand’s Paradox 77 The Suggested Link between the Classical and the New Definitions of Probability 79 Summary of Objections to the Classical Defimtion 80 Objections to My Theory 81 Fmite Collectives 82 Testing Probability Statements 84 An Objection to the First Postulate 86 Objections to the Condition of Randomness 87 Restricted Randomness 89 Meaning of the Condition of Randomness 91 Consistency of the Randomness Axiom 92 A Problem of Terminology 93 Objections to the Frequency Concept 94 Theory of the Plausibility of Statements 95 The Nihilists 97 Restriction to One Single Initial Collective 98 Probability as Part of the Theory of Sets 99 Development of the Frequency Theory 101 Summary and Conclusion 102 CONTENTS fourth lecture The Laws of Large Numbers Poisson’s Two Different Propositions 104 Equally Likely Events 106 Arithmetical Explanation 107 Subsequent Frequency Definition 109 The Content of Poisson’s Theorem 1 lo Example of a Sequence to which Poisson’s Theorem does not Apply 111 Bernoulli and non-Bernoulli Sequences 112 Derivation of the Bernoulli-Poisson Theorem 113 Summary 115 Inference 1 1 6 Bayes’s Problem 117 Initial and Inferred Probability 118 Longer Sequences of Trials 120 Independence of the Initial Distribution 122 The Relation of Bayes’s Theorem to Poisson’s Theorem 124 The Three Propositions 125 Generalization of the Laws of Large Numbers 125 The Strong Law of Large Numbers 127 The Statistical Functions 129 The First Law of Large Numbers for Statistical Functions 131 The Second Law of Large Numbers for Statistical Functions 1 32 Closing Remarks 133 FIFTH LECTURE Application in Statistics and the Theory of Errors What is Statistics ? 135 Games of Chance and Games of Skill 136 Marbe’s ‘Uniformity in the World’ 138 Answer to Marbe’s Problem 139 Theory of Accumulation and the Law of Series 141 Linked Events 142 The General Purpose of Statistics 144 Lexis’ Theory of Dispersion 145 The Mean and the Dispersion 146 Comparison between the Observed and the Expected Variance 148 Lexis’ Theory and the Laws of Large Numbers 149 Normal and Nonnormal Dispersion 151 Sex Distribution of Infants 1 52 Statistics of Deaths with Supernormal Dispersion 153 Solidarity of Cases 154 Testing Hypotheses 1 55 R. A. Fisher’s ‘Likelihood’ 157 Small Sample Theory 158 Social and Biological Statistics 160 Mendel’s Theory of Heredity 160 Industrial and Technological Statistics 161 An Example of Faulty Statistics 162 Correction 163 Some Results Summarized 165 CONTENTS Descriptive Statistics 166 Foundations of the Theory of Errors 167 Gallon’s Board 169 Normal Curve 1 70 Laplace’s Law 171 The Application of the Theory of Errors 172 SIXTH LECTURE Statistical Problems in Physics The Second Law of Thermodynamics 174 Determinism and Probability 175 Chance Mechanisms 177 Random Fluctuations 178 Small Causes and Large Eflfects 179 Kinetic Theory of Gases 181 Order of Magnitude of ‘Improbability’ 183 Criticism of the Gas Theory 184 Brownian Motion 186 Evolution of Phenomena in Time 187 Probability ‘After-Etfects’ 188 Residence Time and Its Prediction 189 Entropy Theorem and Markoff Chains 192 Svedberg’s Experiments 194 Radioactivity 195 Prediction of Time Intervals 197 Marsden’s and Barratt’s Experiments 198 Recent Development in the Theory of Gases 199 Degeneration of Gases: Electron Theory of Metals 200 Quantum Theory 202 Statistics and Causality 203 Causal Explanation in Newton’s Sense 204 Limitations of Newtonian Mechanics 206 Simplicity as a Cnterion of Causality 208 Giving up the Concept of Causality 209 The Law of Causality 210 New Quantum Statistics 211 Are Exact Measurements Possible? 213 Position and Velocity of a Material Particle 214 Heisenberg’s Uncertainty Principle 215 Consequences for our Physical Concept of the World 217 Final Considerations 218 SUMMARY OF THE SIX LECTURES IN SIXTEEN PROPOSITIONS 221 NOTES AND ADDENDA 224 SUBJECT INDEX 237 NAME INDEX 243
520			_aPREFACE THE present second English edition is not merely a reprinting of the first edition, which has been out of print for several years, but rather a translation of the third German edition, revised by the author in 1951; this last differs in many ways from the second German edition, on which the original Enghsh translation was based. The change consists essentially in the author’s omitting some of the discussions of the early controversies regarding his theory, and making instead various additions: The concept of randomness, which plays a central role in the author’s theory, is reconsidered — in particular, with respect to the problem of mathematical consistency — and carefully reformulated. The question of substituting for it some ‘limited randomness’ is taken up, and the author concludes that, as far as the basic axioms are concerned, no such restriction is advisable. Systematic consideration is given to recent work concerned with the basic definitions of probability theory: in the ideas of E. Tomier and of J. L. Doob, the author sees a remarkable development of his theory of frequencies in collectives. The analysis of the two Laws of Large Numbers has often been considered an outstanding section of the book; in the 1951 edition, on the basis of new mathematical results, the discussion of the Second Law is deepened and enlarged, with the aim of clarifying this highly controversial subject. Comments are added on the testing of hypotheses, (as based on the inference theory originated by T. Bayes), on R. A. Fisher’s ‘likelihood’, and on a few related subjects. These and all other additions are selected as well as discussed in relation to the basic ideas advanced in the book. The deviations in content of the present Enghsh version from the third German edition are insignificant. Some passages which seemed of more local (Austrian) interest have been omitted. In a few instances the text has been changed (with explanation in the Notes when necessary). The Notes, historical, bibliographical, etc., have been somewhat modified. References have been brought up to date; indications of German translations have been replaced by corresponding English works; several notes are new. A subject index has been added. The present text is based on the excellent translation (1939) of Messrs. J. Neyman, D. Scholl, and E. Rabinowitsch; it has been supplemented by all the new material in the 1951 edition, and amended in the light of notes made by the author in anticipation of a new English edition. In addition, the entire text was given a careful editorial revision. The sixth chapter, on ‘Statistics in Physics’ was essentially retranslated. In these various aspects, and in particular with regard to the new translations, I enjoyed the valuable assistance of Mrs. R. Buka. My sincere thanks go to Professor J, Neyman for his understanding encouragement, to Professor E. Tornier for significant advice regarding a few difficult passages, to Dr. A. O’Neill who prepared the index, to Mr. F. J. Zucker, who kindly read the translation of the sixth chapter, and to Mr. J. D. Elder, who was good enough to check the text with respect to uniformity and general consistency of style. I am very grateful to the Department of Mathematics, particularly to Professor G. Birkhoff, and to the Division of Engineering and Applied Physics of Harvard University, who together with the Office of Naval Research sponsored this work. Finally, I thank the publishers, Allen & Unwin, Ltd., London, and the Macmillan Company, New York, for the cooperation they gave freely whenever needed, and the Springer-Verlag, Vienna, for granting permission to bring out this edition.
650			_aProbabilities. _96708
650			_aMathematical statistics. _96709
700			_aBall, Samuel _eauthor _911214
856			_uhttps://archive.org/details/in.ernet.dli.2015.189506/mode/1up
942			_2ddc _cBK _h004.422 M687 _n0
999			_c4594 _d4594