| Description |
1 online resource (363 pages) |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Preface; Table of Contents; References; Chapter 1: Probability; 1.1 Introduction; 1.2 Models in General; 1.3 The Frequency Approach Rejected; 1.4 The Single Event Model; 1.5 Symmetry as the Measure of Probability; 1.5-1 Selected faces of a die; 1.5-2 A card with the face 7; 1.5-3 Probability of a spade; 1.6 Independence; 1.6-1 The sample space of two dice; 1.6-2 The sample space of three coins; 1.6-3 The number of paths; 1.7 Subsets of a Sample Space; 1.7-1 Exactly one head in three tosses of three coins; 1.7-2 Sum of two dice |
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Aside: Probability scales1.8 Conditional Probability; 1.8-1 At least two heads in ten tosses; 1.8-2 An even sum on two dice; 1.8-3 Probability of exactly three heads given that there are at least two heads; 1.9 Randomness; 1.9-1 The two gold coin problem; 1.9-2 The two children problem; 1.9-3 The four card deck; 1.9-4 The two headed coin; 1.9-5 No information; 1.9-6 The birthday problem; 1.9-7 The general case of coincidences; 1.9-8 The information depends on your state of knowledge; 1.10 Critique of the Model; 1.A Bounds on Sums; 1.B A Useful Bound; Chapter 2: Some Mathematical Tools |
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2.1 Introduction2.2 Permutations; 2.2-1 Arrange 3 books on a shelf; 2.2-2 Arrange 6 books on a shelf; 2.2-3 Arrange 10 books on a shelf; 2.2-4 Two out of three items identical; 2.2-5 Another case of identical items; 2.3 Combinations; 2.3-1 Sums of binomial coefficients; 2.3-2 Bridge hands; 2.3-3 3 out of 7 books; 2.3-4 Probability of n heads in 2n tosses of a coin; 2.3-5 Probability of a void in bridge; 2.3-6 Similar items in bins; 2.3-7 With at least 1 in each bin; 2.4 The Binomial Distributionâ#x80;#x93;Bernoulli Trials; 2.4-1 Inspection of parts; 2.4-2 Continued; 2.4-3 Floppy discs |
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2.4-4 Distribution of the sum of three dice2.4-5 Bose-Einstein statistics; 2.4-6 Fermi-Dirac statistics; 2.5 Random Variables, Mean and the Expected Value; 2.5-1 Expected value of a roll of a die; 2.5-2 Expected value of a coin toss; 2.5-3 Sum of two dice; 2.5-4 Gambling on an unknown bias; Mathematical aside: Sums of powers of the integers; 2.6 The Variance; 2.6-1 Variance of a die; 2.6-2 Variance of M equally likely outcomes; 2.6-3 Variance of the sum of n dice; 2.7 The Generating Function; 2.7-1 Mean and variance of the binomial distribution; 2.7-2 The binomial distribution again |
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2.7-3 The distribution of the sum of three dice2.8 The Weak Law of Large Numbers; 2.9 The Statistical Assignment of Probability; 2.9-1 Test of coin and Monte Carlo methods; 2.9-2 Chevalier de Mere problem; 2.10 The Representation of Information; 2.11 Summary; 2.A Derivation of the Weak Law of Large Numbers; 2.B Useful Binomial Identities; Chapter 3: Methods for Solving Problems; 3.1 The Five Methods; 3.1-1 The elevator problem (five ways); 3.2 The Total Sample Space and Fair Games; 3.2-1 Matching pennies (coins); 3.2-2 Biased coins; 3.2-3 Raffles and lotteries |
| Summary |
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, The Art of Probability is filled with unique insights and tricks worth knowing |
| Notes |
3.2-4 How many tickets to buy in a raffle |
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Print version record |
| Subject |
Probabilities.
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Mathematics -- Applied
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Mathematics -- Probability and Statistics -- General
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Probability
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probability.
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Probabilities
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| Form |
Electronic book
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| ISBN |
9780429961502 |
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0429961502 |
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