eBook Math Explained: The Britannica Guide to Statistics and Probability, 1st Edition

  • Published By:
  • ISBN-10: 161530228X
  • ISBN-13: 9781615302284
  • DDC: 519.2
  • Grade Level Range: 9th Grade - 12th Grade
  • 288 Pages | eBook
  • Original Copyright 2011 | Published/Released April 2012
  • This publication's content originally published in print form: 2011
  • Price:  Sign in for price

About

Overview

By observing patterns and repeated behaviors, mathematicians have devised calculations to significantly reduce human potential for error. This volume introduces the historical and mathematical basis of statistics and probability as well as their application to everyday situations. Readers will also meet the prominent thinkers who advanced the field and established a numerical basis for prediction.

Table of Contents

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.