BOOK COVER -- TITLE -- COPYRIGHT -- CONTENTS -- INTRODUCTION -- CHAPTER 1 HISTORY OF STATISTICS AND PROBABILITY -- EARLY PROBABILITY -- GAMES OF CHANCE -- RISKS, EXPECTATIONS, AND FAIR CONTRACTS -- PROBABILITY AS THE LOGIC OF UNCERTAINTY -- THE PROBABILITY OF CAUSES -- THE RISE OF STATISTICS -- POLITICAL ARITHMETIC -- SOCIAL NUMBERS -- A NEW KIND OF REGULARITY -- STATISTICAL PHYSICS -- THE SPREAD OF STATISTICAL MATHEMATICS -- STATISTICAL THEORIES IN THE SCIENCES -- BIOMETRY -- SAMPLES AND EXPERIMENTS -- THE MODERN ROLE OF STATISTICS -- CHAPTER 2 PROBABILITY THEORY -- EXPERIMENTS, SAMPLE SPACE, EVENTS, AND EQUALLY LIKELY PROBABILITIES -- APPLICATIONS OF SIMPLE PROBABILITY EXPERIMENTS -- THE PRINCIPLE OF ADDITIVITY -- MULTINOMIAL PROBABILITY -- THE BIRTHDAY PROBLEM -- CONDITIONAL PROBABILITY -- APPLICATIONS OF CONDITIONAL PROBABILITY -- INDEPENDENCE -- BAYES'S THEOREM -- RANDOM VARIABLES, DISTRIBUTIONS, EXPECTATION, AND VARIANCE -- RANDOM VARIABLES -- PROBABILITY DISTRIBUTION -- EXPECTED VALUE -- VARIANCE -- AN ALTERNATIVE INTERPRETATION OF PROBABILITY -- THE LAW OF LARGE NUMBERS, THE CENTRAL LIMIT THEOREM, AND THE POISSON APPROXIMATION -- THE LAW OF LARGE NUMBERS -- THE CENTRAL LIMIT THEOREM -- THE POISSON APPROXIMATION -- INFINITE SAMPLE SPACES AND AXIOMATIC PROBABILITY -- INFINITE SAMPLE SPACES -- THE STRONG LAW OF LARGE NUMBERS -- MEASURE THEORY -- PROBABILITY DENSITY FUNCTIONS -- CONDITIONAL EXPECTATION AND LEAST SQUARES PREDICTION -- THE POISSON PROCESS AND THE BROWNIAN MOTION PROCESS -- THE POISSON PROCESS -- BROWNIAN MOTION PROCESS -- STOCHASTIC PROCESSES -- STATIONARY PROCESSES -- MARKOVIAN PROCESSES -- THE EHRENFEST MODEL OF DIFFUSION -- THE SYMMETRIC RANDOM WALK -- QUEUING MODELS -- INSURANCE RISK THEORY -- MARTINGALE THEORY -- CHAPTER 3 STATISTICS -- DESCRIPTIVE STATISTICS -- TABULAR METHODS -- GRAPHICAL METHODS -- NUMERICAL MEASURES.

PROBABILITY -- EVENTS AND THEIR PROBABILITIES -- RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS -- SPECIAL PROBABILITY DISTRIBUTIONS -- ESTIMATION -- SAMPLING AND SAMPLING DISTRIBUTIONS -- ESTIMATION OF A POPULATION MEAN -- ESTIMATION OF OTHER PARAMETERS -- ESTIMATION PROCEDURES FOR TWO POPULATIONS -- HYPOTHESIS TESTING -- BAYESIAN METHODS -- EXPERIMENTAL DESIGN -- ANALYSIS OF VARIANCE AND SIGNIFICANCE TESTING -- REGRESSION AND CORRELATION ANALYSIS -- TIME SERIES AND FORECASTING -- NONPARAMETRIC METHODS -- STATISTICAL QUALITY CONTROL -- ACCEPTANCE SAMPLING -- STATISTICAL PROCESS CONTROL -- SAMPLE SURVEY METHODS -- DECISION ANALYSIS -- CHAPTER 4 GAME THEORY -- CLASSIFICATION OF GAMES -- ONE-PERSON GAMES -- TWO-PERSON CONSTANT-SUM GAMES -- GAMES OF PERFECT INFORMATION -- GAMES OF IMPERFECT INFORMATION -- MIXED STRATEGIES AND THE MINIMAX THEOREM -- UTILITY THEORY -- TWO-PERSON VARIABLE-SUM GAMES -- COOPERATIVE VERSUS NONCOOPERATIVE GAMES -- THE NASH SOLUTION -- THE PRISONERS' DILEMMA -- SEQUENTIAL AND SIMULTANEOUS TRUELS -- POWER IN VOTING: THE PARADOX OF THE CHAIR'S POSITION -- THE VON NEUMANN-MORGENSTERN THEORY -- THE BANZHAF VALUE IN VOTING GAMES -- CHAPTER 5 COMBINATORICS -- HISTORY -- EARLY DEVELOPMENTS -- COMBINATORICS DURING THE 20TH CENTURY -- PROBLEMS OF ENUMERATION -- PERMUTATIONS AND COMBINATIONS -- RECURRENCE RELATIONS AND GENERATING FUNCTIONS -- PARTITIONS -- THE FERRERS DIAGRAM -- THE PRINCIPLE OF INCLUSION AND EXCLUSION: DERANGEMENTS -- POLYA'S THEOREM -- THE MÖBIUS INVERSION THEOREM -- SPECIAL PROBLEMS -- PROBLEMS OF CHOICE -- SYSTEMS OF DISTINCT REPRESENTATIVES -- RAMSEY'S NUMBERS -- DESIGN THEORY -- BIB (BALANCED INCOMPLETE BLOCK) DESIGNS -- PBIB (PARTIALLY BALANCED INCOMPLETE BLOCK) DESIGNS -- LATIN SQUARES AND THE PACKING PROBLEM -- ORTHOGONAL LATIN SQUARES -- ORTHOGONAL ARRAYS AND THE PACKING PROBLEM -- GRAPH THEORY -- DEFINITIONS.

ENUMERATION OF GRAPHS -- CHARACTERIZATION PROBLEMS OF GRAPH THEORY -- APPLICATIONS OF GRAPH THEORY -- PLANAR GRAPHS -- THE FOUR-COLOUR MAP PROBLEM -- EULERIAN CYCLES AND THE KÖNIGSBERG BRIDGE PROBLEM -- DIRECTED GRAPHS -- COMBINATORIAL GEOMETRY -- SOME HISTORICALLY IMPORTANT TOPICS OF COMBINATORIAL GEOMETRY -- METHODS OF COMBINATORIAL GEOMETRY -- CHAPTER 6 BIOGRAPHIES -- JEAN LE ROND D'ALEMBERT -- THOMAS BAYES -- DANIEL BERNOULLI -- JAKOB BERNOULLI -- BHASKARA II -- LUDWIG EDUARD BOLTZMANN -- GEORGE BOOLE -- GIROLAMO CARDANO -- ART HUR CAYLEY -- FRANCIS YSIDRO EDGEWORTH -- PIERRE DE FERMAT -- SIR RONALD AYLMER FISHER -- JOHN GRAUNT -- PIERRE-SIMON, MARQUIS DE LAPLACE -- ADRIEN-MARIE LEGENDRE -- ABRAHAM DE MOIVRE -- JOHN F. NASH, JR. -- JERZY NEYMAN -- KARL PEARSON -- SIR WILLIAM PETTY -- SIMÉON-DENIS POISSON -- ADOLPHE QUETELET -- JAKOB STEINER -- JAMES JOSEPH SYLVESTER -- JOHN VON NEUMANN -- CHAPTER 7 SPECIAL TOPICS -- BAYES'S THEOREM -- BINOMIAL DISTRIBUTION -- CENTRAL LIMIT THEOREM -- CHEBYSHEV'S INEQUALITY -- DECISION THEORY -- DISTRIBUTION FUNCTION -- ERROR -- ESTIMATION -- INDIFFERENCE -- INFERENCE -- INTERVAL ESTIMATION -- LAW OF LARGE NUMBERS -- LEAST SQUARES APPROXIMATION -- MARKOV PROCESS -- MEAN -- NORMAL DISTRIBUTION -- PERMUTATIONS AND COMBINATIONS -- POINT ESTIMATION -- POISSON DISTRIBUTION -- QUEUING THEORY -- RANDOM WALK -- SAMPLING -- STANDARD DEVIATION -- STOCHASTIC PROCESS -- STUDENT'S T-TEST -- GLOSSARY -- BIBLIOGRAPHY -- GENERAL WORKS -- PROBABILITY THEORY -- STATISTICS -- GAME THEORY -- INDEX -- BACK COVER.