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Basic Probability Theory (Paperba

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  • Àú : Ash, Robert B.
  • ÃâÆÇ»ç : Dover
  • ¹ßÇà : 2008³â 06¿ù 26ÀÏ
  • Âʼö : 337
  • ISBN : 9780486466286
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Basic Concepts
Introductionp. 1
Algebra of Events (Boolean Algebra)p. 3
Probabilityp. 10
Combinatorial Problemsp. 15
Independencep. 25
Conditional Probabilityp. 33
Some Fallacies in Combinatorial Problemsp. 39
Appendix: Stirling's Formulap. 43
Random Variables
Introductionp. 46
Definition of a Random Variablep. 48
Classification of Random Variablesp. 51
Functions of a Random Variablep. 58
Properties of Distribution Functionsp. 66
Joint Density Functionsp. 70
Relationship Between Joint and Individual Densities; Independence of Random Variablesp. 76
Functions of More Than One Random Variablep. 85
Some Discrete Examplesp. 95
Expectation
Introductionp. 100
Terminology and Examplesp. 107
Properties of Expectationp. 114
Correlationp. 119
The Method of Indicatorsp. 122
Some Properties of the Normal Distributionp. 124
Chebyshev's Inequality and the Weak Law of Large Numbersp. 126
Conditional Probability and Expectation
Introductionp. 130
Examplesp. 133
Conditional Density Functionsp. 135
Conditional Expectationp. 140
Appendix: The General Concept of Conditional Expectationp. 152
Characteristic Functions
Introductionp. 154
Examplesp. 158
Properties of Characteristic Functionsp. 166
The Central Limit Theoremp. 169
Infinite Sequences of Random Variables
Introductionp. 178
The Gambler's Ruin Problemp. 182
Combinatorial Approach to the Random Walk; the Reflection Principlep. 186
Generating Functionsp. 191
The Poisson Random Processp. 196
The Strong Law of Large Numbersp. 203
Markov Chains
Introductionp. 211
Stopping Times and the Strong Markov Propertyp. 217
Classification of Statesp. 220
Limiting Probabilitiesp. 230
Stationary and Steady-State Distributionsp. 236
Introduction to Statistics
Statistical Decisionsp. 241
Hypothesis Testingp. 243
Estimationp. 258
Sufficient Statisticsp. 264
Unbiased Estimates Based on a Complete Sufficient Statisticp. 268
Sampling from a Normal Populationp. 274
The Multidimensional Gaussian Distributionp. 279
Tablesp. 286
A Brief Bibliographyp. 289
Solutions to Problemsp. 290
Indexp. 333
Table of Contents provided by Ingram. All Rights Reserved.

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This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.

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