Front Cover.

Half Title Page.

Title Page.

Copyright Page.

Contents.

Introduction.

1: History of Statistics and Probability.

2: Early Probability.

3: Games of Chance.

4: Risks, Expectations, and Fair Contracts.

5: Probability as the Logic of Uncertainty.

6: The Probability of Causes.

7: The Rise of Statistics.

8: Political Arithmetic.

9: Social Numbers.

10: A New Kind of Regularity.

11: Statistical Physics.

12: The Spread of Statistical Mathematics.

13: Statistical Theories in the Sciences.

14: Biometry.

15: Samples and Experiments.

16: The Modern Role of Statistics.

17: Probability Theory.

18: Experiments, Sample Space, Events, and Equally Likely Probabilities.

19: Applications of Simple Probability Experiments.

20: The Principle of Additivity.

21: Multinomial Probability.

22: The Birthday Problem.

23: Conditional Probability.

24: Applications of Conditional Probability.

25: Independence.

26: Bayes's Theorem.

27: Random Variables, Distributions, Expectation, and Variance.

28: Random Variables.

29: Probability Distribution.

30: Expected Value.

31: Variance.

32: An Alternative Interpretation of Probability.

33: The Law of Large Numbers, the Central Limit Theorem, and the Poisson Approximation.

34: The Law of Large Numbers.

35: The Central Limit Theorem.

36: The Poisson Approximation.

37: Infinite Sample Spaces and Axiomatic Probability.

38: Infinite Sample Spaces.

39: The Strong Law of Large Numbers.

40: Measure Theory.

41: Probability Density Functions.

42: Conditional Expectation and Least Squares Prediction.

43: The Poisson Process and the Brownian Motion Process.

44: The Poisson Process.

45: Brownian Motion Process.

46: Stochastic Processes.

47: Stationary Processes.

48: Markovian Processes.

49: The Ehrenfest Model of Diffusion.

50: The Symmetric Random Walk.

51: Queuing Models.

52: Insurance Risk Theory.

53: Martingale Theory.

54: Statistics.

55: Descriptive Statistics.

56: Tabular Methods.

57: Graphical Methods.

58: Numerical Measures.

59: Probability.

60: Events and Their Probabilities.

61: Random Variables and Probability Distributions.

62: Special Probability Distributions.

63: Estimation.

64: Sampling and Sampling Distributions.

65: Estimation of a Population Mean.

66: Estimation of Other Parameters.

67: Estimation Procedures for Two Populations.

68: Hypothesis Testing.

69: Bayesian Methods.

70: Experimental Design.

71: Analysis of Variance and Significance Testing.

72: Regression and Correlation Analysis.

73: Time Series and Forecasting.

74: Nonparametric Methods.

75: Statistical Quality Control.

76: Acceptance Sampling.

77: Statistical Process Control.

78: Sample Survey Methods.

79: Decision Analysis.

80: Game Theory.

81: Classification of Games.

82: One-Person Games.

83: Two-Person Constant-Sum Games.

84: Games of Perfect Information.

85: Games of Imperfect Information.

86: Mixed Strategies and the Minimax Theorem.

87: Utility Theory.

88: Two-Person Variable-Sum Games.

89: Cooperative versus Noncooperative Games.

90: The Nash Solution.

91: The Prisoners' Dilemma.

92: N-Person Games.

93: Sequential and Simultaneous Truels.

94: Power in Voting: The Paradox of the Chair's Position.

95: The von Neumann–Morgenstern Theory.

96: The Banzhaf Value in Voting Games.

97: Combinatorics.

98: History.

99: Early Developments.

100: Combinatorics During the 20th Century.

101: Problems of Enumeration.

102: Permutations and Combinations.

103: Recurrence Relations and Generating Functions.

104: Partitions.

105: The Ferrers Diagram.

106: The Principle of Inclusion and Exclusion: Derangements.

107: Polya's Theorem.

108: The Möbius Inversion Theorem.

109: Special Problems.

110: Problems of Choice.

111: Systems of Distinct Representatives.

112: Ramsey's Numbers.

113: Design Theory.

114: BIB (Balanced Incomplete Block) Designs.

115: PBIB (Partially Balanced Incomplete Block) Designs.

116: Latin Squares and the Packing Problem.

117: Orthogonal Latin Squares.

118: Orthogonal Arrays and the Packing Problem.

119: Graph Theory.

120: Definitions.

121: Enumeration of Graphs.

122: Characterization Problems of Graph Theory.

123: Applications of Graph Theory.

124: Planar Graphs.

125: The Four-Colour Map Problem.

126: Eulerian Cycles and the Königsberg Bridge Problem.

127: Directed Graphs.

128: Combinatorial Geometry.

129: Some Historically Important Topics of Combinatorial Geometry.

130: Methods of Combinatorial Geometry.

131: Biographies.

132: Jean Le Rond D'Alembert.

133: Thomas Bayes.

134: Daniel Bernoulli.

135: Jakob Bernoulli.

136: Bhāskara II.

137: Ludwig Eduard Boltzmann.

138: George Boole.

139: Girolamo Cardano.

140: Arthur Cayley.

141: Francis Ysidro Edgeworth.

142: Pierre de Fermat.

143: Sir Ronald Aylmer Fisher.

144: John Graunt.

145: Pierre-Simon, Marquis de Laplace.

146: Adrien-Marie Legendre.

147: Abraham de Moivre.

148: John F. Nash, Jr..

149: Jerzy Neyman.

150: Karl Pearson.

151: Sir William Petty.

152: Siméon-Denis Poisson.

153: Adolphe Quetelet.

154: Jakob Steiner.

155: James Joseph Sylvester.

156: John Von Neumann.

157: Special Topics.

158: Bayes's Theorem.

159: Binomial Distribution.

160: Central Limit Theorem.

161: Chebyshev's Inequality.

162: Decision Theory.

163: Distribution Function.

164: Error.

165: Estimation.

166: Indifference.

167: Inference.

168: Interval Estimation.

169: Law of Large Numbers.

170: Least Squares Approximation.

171: Markov Process.

172: Mean.

173: Normal Distribution.

174: Permutations and Combinations.

175: Point Estimation.

176: Poisson Distribution.

177: Queuing Theory.

178: Random Walk.

179: Sampling.

180: Standard Deviation.

181: Stochastic Process.

182: Student's T-Test.

Glossary.

Bibliography.

Index.