Preface | p. xi |
The Nature of Chance | p. 3 |
Silk, Strength, and Statistics | p. 3 |
What Is Certain? | p. 7 |
Determinism versus Chance | p. 8 |
Chaos | p. 9 |
A Road Map | p. 11 |
Rules of Disorder | p. 12 |
Events, Experiments, and Outcomes | p. 12 |
Sarcastic Fish | p. 13 |
Bipolar Smut | p. 14 |
Discrete versus Continuous | p. 17 |
Drawing Pictures | p. 18 |
Probability | p. 19 |
Rules and Tools | p. 20 |
Events Are the Sum of Their Parts | p. 20 |
The Union of Sets | p. 21 |
The Probability of a Union | p. 23 |
Probability and the Intersection of Sets | p. 24 |
The Complement of a Set | p. 25 |
Additional Information and Conditional Probabilities | p. 27 |
Bayes' Formula | p. 29 |
AIDS and Bayes' Formula | p. 30 |
The Independence of Sets | p. 32 |
Probability Distributions | p. 34 |
Summary | p. 37 |
Problems | p. 37 |
Discrete Patterns of Disorder | p. 40 |
Random Variables | p. 40 |
Expectations Defined | p. 42 |
The Variance | p. 46 |
The Trials of Bernoulli | p. 48 |
Beyond 0's and 1's | p. 50 |
Bernoulli = Binomial | p. 51 |
Permutations and Combinations | p. 53 |
Waiting Forever | p. 60 |
Summary | p. 65 |
Problems | p. 66 |
Continuous Patterns of Disorder | p. 68 |
The Uniform Distribution | p. 69 |
The Cumulative Probability Distribution | p. 70 |
The Probability Density Function | p. 71 |
The Expectation | p. 74 |
The Variance | p. 76 |
The Shape of Distributions | p. 77 |
The Normal Curve | p. 79 |
Why Is the Normal Curve Normal? | p. 82 |
The Cumulative Normal Curve | p. 84 |
The Standard Error | p. 86 |
A Brief Detour to Statistics | p. 89 |
Summary | p. 92 |
Problems | p. 93 |
Appendix 1: The Normal Distribution | p. 94 |
Appendix 2: The Central Limit Theorem | p. 98 |
Random Walks | p. 106 |
The Motion of Molecules | p. 106 |
Rules of a Random Walk | p. 110 |
The Average | p. 110 |
The Variance | p. 112 |
Diffusive Speed | p. 115 |
Diffusion and the Real World | p. 115 |
A Digression on the Binomial Theorem | p. 117 |
The Biology of Diffusion | p. 119 |
Fick's Equation | p. 123 |
A Use of Fick's Equation: Limits to Size | p. 126 |
Receptors and Channels | p. 130 |
Summary | p. 136 |
Problems | p. 137 |
More Random Walks | p. 139 |
Diffusion to Capture | p. 139 |
Two Absorbing Walls | p. 142 |
One Reflecting Wall | p. 144 |
Adrift at Sea: Turbulent Mixing of Plankton | p. 145 |
Genetic Drift | p. 148 |
A Genetic Diffusion Coefficient | p. 149 |
Drift and Fixation | p. 151 |
Genetic Drift and Irreproducible Pigs | p. 154 |
The Biology of Elastic Materials | p. 156 |
Elasticity Defined | p. 156 |
Biological Rubbers | p. 157 |
The Limits to Energy Storage | p. 161 |
Random Walks in Three Dimensions | p. 163 |
Random Protein Configurations | p. 167 |
A Segue to Thermodynamics | p. 169 |
Summary | p. 173 |
Problems | p. 173 |
The Statistics of Extremes | p. 175 |
The Danger of Cocktail Parties | p. 175 |
Calculating the Maximum | p. 182 |
Mean and Modal Maxima | p. 185 |
Ocean Waves | p. 186 |
The Statistics of Extremes | p. 189 |
Life and Death in Rhode Island | p. 194 |
Play Ball! | p. 196 |
A Note on Extrapolation | p. 204 |
Summary | p. 206 |
Problems | p. 206 |
Noise and Perception | p. 208 |
Noise Is Inevitable | p. 208 |
Dim Lights and Fuzzy Images | p. 212 |
The Poisson Distribution | p. 213 |
Bayes' Formula and the Design of Rods | p. 218 |
Designing Error-Free Rods | p. 219 |
The Origin of Membrane Potentials | p. 220 |
Membrane Potential in Rod Cells | p. 222 |
Noise and Ion Channels | p. 225 |
An Electrical Analog | p. 226 |
Calculating the Membrane Voltage | p. 227 |
Calculating the Size | p. 229 |
Noise and Hearing | p. 230 |
Fluctuations in Pressure | p. 231 |
The Rate of Impact | p. 232 |
Fluctuations in Velocity | p. 233 |
Fluctuations in Momentum | p. 235 |
The Standard Error of Pressure | p. 235 |
Quantifying the Answer | p. 236 |
The Rest of the Story | p. 239 |
Stochastic Resonance | p. 239 |
The Utility of Noise | p. 239 |
Nonl | |
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