Introduction to mathematical probability

Title Page......Page 1
Preface......Page 3
CONTENTS......Page 5
INTRODUCTION......Page 9
I. COMPUTATION OF PROBABILITIES BY DIRECT ENUMERATION OF CASES......Page 22
II. THEOREMS OF TOTAL AND COMPOUND PROBABILITY......Page 35
III. REPEATED TRIALS......Page 52
IV. PROBABILITIES OF HYPOTHESES AND BAYES' THEOREM......Page 68
V. USE OF DIFFERENCE EQUATIONS IN SOLVING PROBLEMS OF PROBABILITY......Page 82
VI. BERNOULLI'S THEOREM......Page 104
VII. APPROXIMATE EVALUATION OF PROBABILITIES IN BERNOULLIAN CASE......Page 127
VIII. FURTHER CONSIDERATIONS ON GAMES OF CHANCE......Page 147
IX. MATHEMATICAL EXPECTATION......Page 169
X. THE LAW OF LARGE NUMBERS......Page 190
XI. APPLICATIONS OF THE LAW OF LARGE NUMBERS......Page 216
XII. PROBABILITIES IN CONTINUUM......Page 243
XIII. THE GENERAL CONCEPT OF DISTRIBUTION......Page 268
XIV. FUNDAMENTAL LIMIT THEOREMS......Page 291
XV. NORMAL DISTRIBUTION IN TWO DIMENSIONS. LIMIT THEOREM FOR SUMS OF INDEPENDENT VECTORS. ORIGIN OF NORMAL CORRELATION......Page 316
XVI. DISTRIBUTION OF CERTAIN FUNCTIONS OF NORMALLY DISTRIBUTED VARIABLES......Page 339
App. I......Page 355
App. II: METHOD OF MOMENTS AND ITS APPLICATIONS......Page 364
App. III: ON A GAUSSIAN PROBLEM......Page 406
Table of the Probability Integral......Page 417
INDEX......Page 419