The Art of Probability: For Scientists and Engineers

Content: 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. 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. 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
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Bernoulli Trials
 2.4-1 Inspection of parts
 2.4-2 Continued
 2.4-3 Floppy discs. 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. 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.