Probably Not: Table of Contents
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Preface |
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1. |
AN INTRODUCTION TO PROBABILITY |
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Predicting the Future / 1 |
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Rule Making / 3 |
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Random Events and Probability / 5 |
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The Lottery {Very Improbable Events and Large Data Sets} / 10 |
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Coin Flipping {Fair Games, Looking Backwards for Insight} /13 |
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The Coin Flipping Strategy that Can’t Lose / 19 |
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The Prize Behind the Door {Looking Backwards for Insight, Again} / 20 |
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The Checkerboard {Dealing With Only Part of the Data Set / 22 |
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2. |
PROBABILITY DISTRIBUTION FUNCTIONS AND SOME BASICS |
27 |
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The Probability Distribution Function / 27 |
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Average and Weighted Averages /32 |
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Expected Values / 35 |
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The Basic Coin Flip Game / 37 |
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The Standard Deviation / 40 |
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The Cumulative Distribution Function / 48 |
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3. |
BUILDING A BELL |
54 |
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4. |
RANDOM WALKS |
67 |
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The One- |
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What Probability Really Means / 75 |
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Diffusion / 77 |
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5. |
LIFE INSURANCE AND SOCIAL SECURITY |
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Insurance as Gambling / 83 |
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Life Tables / 83 |
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Birth Rates and Population Stability / 90 |
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Life Tables Again / 91 |
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Premiums / 94 |
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Social Security - |
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6. |
BINOMIAL PROBABILITIES |
104 |
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The Binomial Probability Formula / 105 |
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Permutations and Combinations / 107 |
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Large Number Approximations / 109 |
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The Poisson Distribution / 112 |
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Disease Clusters / 114 |
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Clusters / 114 |
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7. |
PSEUDORANDOM NUMBERS AND MONTE CARLO SIMULATIONS |
117 |
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Pseudorandom Numbers / 118 |
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The Middle Squares PSNG / 119 |
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The Linear Congruential PSNG / 121 |
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An Arbitrary Distribution Generator / 124 |
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Monte Carlo Simulations / 126 |
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A League of Our Own / 132 |
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8. |
SOME GAMBLING GAMES IN DETAIL |
136 |
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The Basic Coin Flip Game / 136 |
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The Gantt Chart / 142 |
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The “Ultimate Winning Strategy” / 144 |
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The Game Show / 150 |
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Parimutuel Betting / 154 |
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9. |
TRAFFIC LIGHTS AND TRAFFIC |
158 |
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Outsmarting a Traffic Light? / 159 |
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Many Lights and Many Cars / 164 |
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Simulating Traffic Flow / 164 |
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Simulation Results / 167 |
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10. |
COMBINED AND CONDITIONAL PROBABILITIES |
178 |
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Functional Notation / 178 |
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Conditional Probability / 183 |
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Medical Test Results / 186 |
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The Shared Birthday Problem / 189 |
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11. |
SCHEDULING AND WAITING |
192 |
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Scheduling Appointments in the Doctor’s Office / 193 |
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Lunch With a Friend / 199 |
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Waiting For a Bus / 204 |
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12. |
STOCK MARKET PORTFOLIOS |
208 |
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13. |
BENFORD, PORRONDO AND SIMPSON |
215 |
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Benford’s Law / 215 |
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Porrondo’s Paradox / 221 |
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Simpson’s Paradox / 228 |
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14. |
NETWORKS, INFECTIOUS DISEASES PROPAGATION, AND CHAIN LETTERS |
234 |
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Degrees of Separation / 235 |
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Propagation Along the Networks / 238 |
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Some Other Uses of Networks / 242 |
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Neighborhood Chains / 249 |
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15. |
BIRD COUNTING |
253 |
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A Walk in the Woods / 253 |
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A Model of Bird Flying Habits / 284 |
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Spotting a Bird / 259 |
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Putting It All Together / 261 |
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16. |
STATISTICAL MECHANICS AND HEAT |
267 |
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Statistical Mechanics / 268 |
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Thermodynamics / 276 |
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17. |
INTRODUCTION TO STATISTICAL ANALYSIS |
280 |
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Sampling / 281 |
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Sample Distributions and Standard Deviations / 283 |
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Estimating Population Average from a Sample / 285 |
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The Student T Distribution / 288 |
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Polling Statistics / 290 |
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Did A Sample Come From A Given Populations / 291 |
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18. |
CHAOS AND QUANTA |
293 |
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Chaos / 293 |
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Probability in Quantum Mechanics / 301 |
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INDEX |
307 |
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