发帖
雷达卡
Everyday Probability a Statistics -Health,.Elections,.Gambling.and.War
Michael M. Woolfson
英文
Contents
Introduction 1
Chapter 1 The Nature of Probability 5
1.1. Probability and Everyday Speech . . . . . . . . . . . . 5
1.2. Spinning a Coin . . . . . . . . . . . . . . . . . . . . . . 6
1.3. Throwing or Spinning Other Objects . . . . . . . . . . 8
Problems 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Chapter 2 Combining Probabilities 13
2.1. Either–or Probability . . . . . . . . . . . . . . . . . . . 13
2.2. Both–and Probability . . . . . . . . . . . . . . . . . . . 15
2.3. Genetically Inherited Disease—Just Gene Dependent 16
2.4. Genetically Dependent Disease—Gender Dependent 19
2.5. A Dice Game—American Craps . . . . . . . . . . . . 21
Problems 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 3 A Day at the Races 25
3.1. Kinds of Probability . . . . . . . . . . . . . . . . . . . . 25
3.2. Betting on a Horse . . . . . . . . . . . . . . . . . . . . . 27
3.3. The Best Conditions for a Punter . . . . . . . . . . . . 31
Problem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Chapter 4 Making Choices and Selections 35
4.1. Children Leaving a Room . . . . . . . . . . . . . . . . 35
4.2. Picking a Team . . . . . . . . . . . . . . . . . . . . . . . 37
4.3. Choosing an Email Username . . . . . . . . . . . . . . 40
4.4. The UK National Lottery . . . . . . . . . . . . . . . . . 41
Problems 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 5 Non-Intuitive Examples of Probability 45
5.1. The Birthday Problem . . . . . . . . . . . . . . . . . . 45
5.2. Crown and Anchor . . . . . . . . . . . . . . . . . . . . 49
5.3. To Switch or Not to Switch—That is the Question . . 52
Problems 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Chapter 6 Probability and Health 55
6.1. Finding the Best Treatment . . . . . . . . . . . . . . . . 55
6.2. Testing Drugs . . . . . . . . . . . . . . . . . . . . . . . 58
Problems 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Chapter 7 Combining Probabilities; The Craps
Game Revealed 67
7.1. A Simple Probability Machine . . . . . . . . . . . . . . 67
7.2. Pontoon—A Card Game . . . . . . . . . . . . . . . . . 70
7.3. The Throwers Chance ofWinning at American Craps 72
Problems 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Chapter 8 The UK National Lottery, Loaded Dice,
and Crooked Wheels 77
8.1. The Need to Test for Fairness . . . . . . . . . . . . . . 77
8.2. Testing Random Numbers . . . . . . . . . . . . . . . . 79
8.3. The UK National Lottery . . . . . . . . . . . . . . . . . 82
8.4. American Craps with Loaded Dice . . . . . . . . . . . 84
8.5. Testing for a Loaded Die . . . . . . . . . . . . . . . . . 89
8.6. The Roulette Wheel . . . . . . . . . . . . . . . . . . . . 91
Problems 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Chapter 9 Block Diagrams 95
9.1. Variation in Almost Everything . . . . . . . . . . . . . 95
9.2. A Shoe Manufacturer . . . . . . . . . . . . . . . . . . . 96
9.3. Histogram Shapes . . . . . . . . . . . . . . . . . . . . . 99
9.4. Lofty and Shorty . . . . . . . . . . . . . . . . . . . . . . 101
Problem 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Chapter 10 The Normal (or Gaussian) Distribution 105
10.1. Probability Distributions . . . . . . . . . . . . . . . . . 105
10.2. The Normal Distribution . . . . . . . . . . . . . . . . . 108
10.3. The Variance and Standard Deviation . . . . . . . . . 110
10.4. Properties of Normal Distributions . . . . . . . . . . . 111
10.5. A Little Necessary Mathematics . . . . . . . . . . . . . 114
10.5.1. Some Special Numbers . . . . . . . . . . . . . . 114
10.5.2. Powers of Numbers . . . . . . . . . . . . . . . . 115
10.6. The Form of the Normal Distribution . . . . . . . . . . 117
10.7. Random and Systematic Errors . . . . . . . . . . . . . 117
10.8. Some Examples of the Normal Distribution . . . . . . 119
10.8.1. Electric Light Bulbs . . . . . . . . . . . . . . . . 119
10.8.2. People on Trolleys and Under-Used Resources 120
Problems 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Chapter 11 Statistics—The Collection and Analysis
of Numerical Data 125
11.1. Too Much Information . . . . . . . . . . . . . . . . . . 125
11.2. AnotherWay of Finding the Variance . . . . . . . . . . 126
11.3. From Regional to National Statistics . . . . . . . . . . 127
Problems 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Chapter 12 The Poisson Distribution and Death
by Horse Kicks 131
12.1. Rare Events . . . . . . . . . . . . . . . . . . . . . . . . 131
12.2. Typing a Manuscript . . . . . . . . . . . . . . . . . . . 133
12.3. The Poisson Distribution as a Formula . . . . . . . . . 135
12.4. Death by Horse Kicks . . . . . . . . . . . . . . . . . . . 137
12.5. Some Other Examples of the Poisson Distribution . . 139
12.5.1. Flying Bomb Attacks on London . . . . . . . . 139
12.5.2. Clustering of a Disease . . . . . . . . . . . . . . 141
12.5.3. Some Further Examples . . . . . . . . . . . . . 142
Problems 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Chapter 13 Predicting Voting Patterns 145
13.1. Election Polls . . . . . . . . . . . . . . . . . . . . . . . . 145
13.2. Polling Statistics . . . . . . . . . . . . . . . . . . . . . . 146
13.3. Combining Polling Samples . . . . . . . . . . . . . . . 149
13.4. Polling with More than Two Parties . . . . . . . . . . . 151
13.5. Factors Affecting Polls and Voting . . . . . . . . . . . 153
Problems 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Chapter 14 Taking Samples—How Many Fish in the Pond? 155
14.1. Why do we Sample? . . . . . . . . . . . . . . . . . . . 155
14.2. Finding out from Samples . . . . . . . . . . . . . . . . 156
14.3. An Illustrative Example . . . . . . . . . . . . . . . . . 158
14.4. General Comments on Sampling . . . . . . . . . . . . 160
14.5. Quality Control . . . . . . . . . . . . . . . . . . . . . . 160
14.6. How Many Fish in the Pond? . . . . . . . . . . . . . . 162
Problems 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Chapter 15 Differences—Rats and IQs 165
15.1. The Significance of Differences . . . . . . . . . . . . . 165
15.2. Significantly Different—So What! . . . . . . . . . . . 167
Problem 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Chapter 16 Crime is Increasing and Decreasing 171
16.1. Crime and the Reporting of Crime . . . . . . . . . . . 171
16.2. The Trend for Overall Crime in England andWales . . 172
16.3. Vehicle Crime, Burglary, and Violent Crime . . . . . . 174
16.4. Homicide . . . . . . . . . . . . . . . . . . . . . . . . . . 177
16.5. Crime and Politicians . . . . . . . . . . . . . . . . . . . 179
Problem 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Chapter 17 My Uncle Joe Smoked 60 a Day 183
17.1. Genetics and Disease . . . . . . . . . . . . . . . . . . . 183
17.2. The Incidence of Smoking in the United Kingdom . . 185
17.3. The Smoking Lottery . . . . . . . . . . . . . . . . . . . 187
Problem 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Chapter 18 Chance, Luck, and Making Decisions 191
18.1. TheWinds of Chance . . . . . . . . . . . . . . . . . . . 191
18.2. Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
18.3. I Want a Lucky General . . . . . . . . . . . . . . . . . . 195
18.4. To Fight or Not to Fight—That is the Question . . . . 197
18.5. The Mathematics ofWar . . . . . . . . . . . . . . . . . 200
Problem 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Solutions to Problems 205
Index 221
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