دانلود کتاب The Art of Probability: For Scientists and Engineers

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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.