| - - - - - - - - - - | |
| 1 | An Introduction To Probability | 5 |
| | Predicting The Future | 5 |
| | Rule Making | 7 |
| | Random Events and Probability | 9 |
| | The Lottery {Very Improbable Events and Large Data Sets} | 15 |
| | Coin Flipping {Fair Games, Looking Backward For Insight} | 17 |
| | The Coin Flipping Strategy That Can't Lose | 24 |
| | The Prize Behind The Door {Looking Backward For Insight, Again} | 25 |
| | The Checkerboard {Dealing With Only Part of the Data Set} | 27 |
| | Comments | 31 |
| | *Problems | 32 |
| | - - - - - - - - - - | |
| 2 | Probability Distribution Functions
and Some Basics | 35 |
| | The Probability Distribution Function | 35 |
| | Average and Weighted Averages | 38 |
| | Expected Values | 41 |
| | The Basic Coin Flip Game | 43 |
| | *PDF Symmetry | 43 |
| | Standard Deviation | 46 |
| | Cumulative Distribution Function | 55 |
| | The Confidence Interval | 57 |
| | Final Points | 58 |
| | *Rehash and Histograms | 59 |
| | *Problems | 66 |
| | - - - - - - - - - - | |
| 3 | Building A Bell | 71 |
| | *Problems | 87 |
| | - - - - - - - - - - | |
| 4 | Random Walks | 89 |
| | The One Dimensional Random Walk | 89 |
| | Some Subsequent Calculations | 93 |
| | Diffusion | 95 |
| | *Problems | 99 |
| | - - - - - - - - - - | |
| 5 | Life Insurance | 103 |
| | Introduction | 103 |
| | Life Insurance | 103 |
| | Insurance As Gambling | 104 |
| | Life Tables | 107 |
| | Birth Rates And Population Stability | 112 |
| | Life Tables, Again | 113 |
| | Premiums | 115 |
| | Social Security - Sooner Or Later? | 120 |
| | *Problems | 124 |
| | - - - - - - - - - - | |
| 6 | The Binomial Theorem | 129 |
| | Introduction | 129 |
| | The Binomial Probability Formula | 130 |
| | Permutations And Combinations | 132 |
| | Large Number Approximations | 134 |
| | The Poisson Equation | 136 |
| | Disease Clusters | 140 |
| | Clusters | 140 |
| | *Problems | 142 |
| | - - - - - - - - - - | |
| 7 | Pseudorandom Numbers and Monte Carlo
Simulations | 145 |
| | Random Numbers and Simulations | 145 |
| | Pseudorandom Numbers | 145 |
| | The Middle Squares PSNG | 146 |
| | The Linear Congruential PSNG | 148 |
| | A Normal Distribution Generator | 150 |
| | An Arbitrary Distribution Generator | 151 |
| | Monte Carlo Simulations | 153 |
| | A League Of Our Own | 156 |
| | Discussion | 159 |
| | *Problems | 160 |
| | - - - - - - - - - - | |
| 8 | Some Gambling Games In Detail | 161 |
| | The Basic Coin Flip Game | 161 |
| | "Ultimate Winning Strategy" | 166 |
| | Parimutuel Betting | 169 |
| | *The Gantt Chart and a Hint of Another Approach | 172 |
| | *Problems | 174 |
| | - - - - - - - - - - | |
| 9 | Scheduling and Waiting | 177 |
| | Introduction | 177 |
| | Scheduling Appointments in the Doctor's Office | 177 |
| | Lunch With A Friend | 180 |
| | Waiting For A Bus | 182 |
| | *Problems | 183 |
| | - - - - - - - - - - | |
| 10 | Combined And Conditional Probabilities | 187 |
| | Introduction | 187 |
| | Functional Notation (Again) | 187 |
| | Conditional Probability | 189 |
| | Medical Test Results | 192 |
| | The Shared Birthday Problem | 195 |
| | *Problems | 197 |
| | - - - - - - - - - - | |
| 11 | Bayesian Statistics | 199 |
| | *Bayes Theorem | 199 |
| | *Multiple Possibilities | 202 |
| | *Will Monty Hall Ever Go Away? | 207 |
| | *Philosophy | 209 |
| | *The Prosecutor's Fallacy | 210 |
| | *Continuous Functions | 211 |
| | *Credible Intervals | 214 |
| | *Gantt Charts (Again) | 215 |
| | *Problems | 217 |
| | - - - - - - - - - - | |
| 12 | Estimation *Problems | 221 |
| | *The Number of Locomotives Problem | 221 |
| | *Number of Locomotives, Improved Estimate | 222 |
| | *Decision Making | 224 |
| | *The Lighthouse Problem | 227 |
| | *The Likelihood Function | 229 |
| | *The Lighthouse Problem II | 232 |
| | - - - - - - - - - - | |
| 13 | Two Paradoxes | 233 |
| | Introduction | 233 |
| | Porrondo's Paradox | 233 |
| | Another Parrondo Game | 236 |
| | The Parrondo Ratchet | 239 |
| | Simpson's Paradox | 240 |
| | *Problems | 244 |
| | - - - - - - - - - - | |
| 14 | Benford's Law | 247 |
| | Introduction | 247 |
| | History | 247 |
| | The 1/x Distribution | 249 |
| | Surface Area of Countries of the World | 252 |
| | *Goodness of Fit Measure | 253 |
| | *Smith'snalysis | 255 |
| | *Problems | 259 |
| | - - - - - - - - - - | |
| 15 | Networks, Infectious Diseases and Chain Letters | 261 |
| | Introduction | 261 |
| | Degrees of Separation | 261 |
| | Propagation Along the Networks | 265 |
| | Some Other Networks | 270 |
| | Neighborhood Chains | 271 |
| | Chain Letters | 273 |
| | Comments | 276 |
| | - - - - - - - - - - | |
| 16 | Introduction To Frequentist Statistical Inference | 277 |
| | Introduction | 277 |
| | Sampling | 277 |
| | Sample Distributions And Standard Deviations | 280 |
| | Estimating Population Average From A Sample | 280 |
| | The Student T Distribution | 285 |
| | *Did A Sample Come From A Given Population? | 289 |
| | *A Little Reconciliation | 289 |
| | *Correlation and Causality | 291 |
| | *Correlation Coefficient | 283 |
| | *Regression Lines | 294 |
| | *Regression to the Mean | 296 |
| | *Problems | 298 |
| | - - - - - - - - - - | |
| 17 | Statistical Mechanics And ThermodynamicsS | 303 |
| | Introduction | 303 |
| | Statistical Mechanics | 304 |
| | (Concepts of) Thermoydynamics | 306 |
| | - - - - - - - - - - | |
| 18 | Chaos And Quanta | 311 |
| | Introduction | 311 |
| | Chaos | 311 |
| | Probability In Quantum Mechanics | 319 |
| | - - - - - - - - - - | |
| | *Appendix | 323 |
| | Index | 329 |
| | - - - - - - - - - - | |
| | *New or Significantly Changed from 1st Edition |
| |
| |
