Richard W. Hamming

The Art Of Probability (eBook, PDF)

• Format: PDF

Produktbeschreibung

Offering accessible and nuanced coverage, Richard W. Hamming discusses theories of probability with unique clarity and depth. Topics covered include the basic philosophical assumptions, the nature of stochastic methods, and Shannon entropy. One of the best introductions to the topic,

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 364
• Erscheinungstermin: 5. März 2018
• Englisch
• ISBN-13: 9780429961502
• Artikelnr.: 54157100

Autorenporträt

Richard W Hamming

Inhaltsangabe

Probability
Introduction
Models in General
The Frequency Approach Rejected
The Single Event Model
Symmetry as the Measure of Probability
Independence
Subsets of a Sample Space
Conditional Probability
Randomness
Critique of the Model Some Mathematical Tools
Permutations
Combinations
The Binomial DistributionBernoulli Trials
Random Variables, Mean and the Expected Value
The Variance
The Generating Function
The Weak Law of Large Numbers
The Statistical Assignment of Probability
The Representation of Information Methods for Solving Problems
The Five Methods
The Total Sample Space and Fair Games
Enumeration
Historical Approach
Recursive Approach
Recursive Approach
The Method of Random Variables
Critique of the Notion of a Fair Game
Bernoulli Evaluation
Robustness
InclusionExclusion Principle Countably Infinite Sample Spaces
Introduction
Bernoulli Trials
On the Strategy to be Adopted
State Diagrams
Generating Functions of State Diagrams
Expanding a Rational Generating Function
Checking the Solution
Paradoxes Continuous Sample Spaces
A Philosophy of the Real Number System
Some First Examples
Some Paradoxes
The Normal Distribution
The Distribution of Numbers
Convergence to the Reciprocal Distribution
Random Times
Dead Times
Poisson Distribution in Time
Queing Theorem
Birth and Death Systems
Summary Uniform Probability Assignments Maximum Entropy
What is Entropy?
Shannons Entropy
Some Mathematical Properties of the Entropy Function
Some Simple Applications
The Maximum Entropy Principle Models of Probability
General Remarks
Maximum Likelihood in a Binary Choice
Von Mises Probability
The Mathematical Approach
The Statistical Approach
When The Mean Does Not Exist
Probability as an Extension of Logic
Di Finetti
Subjective Probability
Fuzzy Probability
Probability in Science
Complex Probability Some Limit Theorems
The Biomial Approximation for th

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Probability * Introduction * Models in General * The Frequency Approach Rejected * The Single Event Model * Symmetry as the Measure of Probability * Independence * Subsets of a Sample Space * Conditional Probability * Randomness * Critique of the Model Some Mathematical Tools * Permutations * Combinations * The Binomial DistributionBernoulli Trials * Random Variables, Mean and the Expected Value * The Variance * The Generating Function * The Weak Law of Large Numbers * The Statistical Assignment of Probability * The Representation of Information Methods for Solving Problems * The Five Methods * The Total Sample Space and Fair Games * Enumeration * Historical Approach * Recursive Approach * Recursive Approach * The Method of Random Variables * Critique of the Notion of a Fair Game * Bernoulli Evaluation * Robustness * InclusionExclusion Principle Countably Infinite Sample Spaces * Introduction * Bernoulli Trials * On the Strategy to be Adopted * State Diagrams * Generating Functions of State Diagrams * Expanding a Rational Generating Function * Checking the Solution * Paradoxes Continuous Sample Spaces * A Philosophy of the Real Number System * Some First Examples * Some Paradoxes * The Normal Distribution * The Distribution of Numbers * Convergence to the Reciprocal Distribution * Random Times * Dead Times * Poisson Distribution in Time * Queing Theorem * Birth and Death Systems * Summary Uniform Probability Assignments Maximum Entropy * What is Entropy? * Shannons Entropy * Some Mathematical Properties of the Entropy Function * Some Simple Applications * The Maximum Entropy Principle Models of Probability * General Remarks * Maximum Likelihood in a Binary Choice * Von Mises Probability * The Mathematical Approach * The Statistical Approach * When The Mean Does Not Exist * Probability as an Extension of Logic * Di Finetti * Subjective Probability * Fuzzy Probability * Probability in Science * Complex Probability Some Limit Theorems * The Biomial Approximation for the case p=1/2 * Approximation by the Normal Distribution * Another Derivation of the Normal Distribution * Random Times * The Zipf Distribution * Summary An Essay on Simulation