Acknowledgments |
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xi | |
About the Companion Website |
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xiii | |
Introduction |
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1 | (4) |
1 An Introduction to Probability |
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5 | (30) |
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5 | (2) |
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7 | (2) |
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Random Events and Probability |
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9 | (6) |
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The Lottery (Very Improbable Events and Very Large Data Sets) |
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15 | (2) |
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Coin Flipping (Fair Games, Looking Backward for Insight) |
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17 | (7) |
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The Coin Flip Strategy That Can't Lose |
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24 | (1) |
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The Prize Behind the Door (Looking Backward for Insight, Again) |
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25 | (2) |
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The Checker Board (Dealing With Only Part of the Data Set( |
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27 | (4) |
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31 | (1) |
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32 | (3) |
2 Probability Distribution Functions and Some Math Basics |
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35 | (36) |
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The Probability Distribution Function |
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35 | (3) |
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Averages and Weighted Averages |
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38 | (3) |
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41 | (2) |
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43 | (1) |
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43 | (3) |
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46 | (9) |
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Cumulative Distribution Function |
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55 | (2) |
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57 | (1) |
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58 | (1) |
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59 | (7) |
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66 | (5) |
3 Building a Bell |
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71 | (18) |
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87 | (2) |
4 Random Walks |
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89 | (14) |
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The One-Dimensional Random Walk |
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89 | (4) |
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Some Subsequent Calculations |
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93 | (2) |
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95 | (4) |
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99 | (4) |
5 Life Insurance |
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103 | (26) |
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103 | (1) |
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103 | (1) |
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104 | (3) |
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107 | (5) |
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Birth Rates and Population Stability |
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112 | (1) |
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113 | (2) |
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115 | (5) |
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Social Security - Sooner or Later? |
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120 | (5) |
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125 | (4) |
6 The Binomial Theorem |
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129 | (16) |
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129 | (1) |
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The Binomial Probability Formula |
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130 | (2) |
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Permutations and Combinations |
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132 | (2) |
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Large Number Approximations |
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134 | (2) |
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136 | (4) |
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140 | (1) |
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140 | (2) |
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142 | (3) |
7 Pseudorandom Numbers and Monte Carlo Simulations |
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145 | (16) |
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Random Numbers and Simulations |
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145 | (1) |
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145 | (1) |
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146 | (2) |
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The Linear Congruential PRNG |
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148 | (2) |
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A Normal Distribution Generator |
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150 | (1) |
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An Arbitrary Distribution Generator |
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151 | (2) |
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153 | (3) |
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156 | (3) |
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159 | (1) |
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160 | (1) |
8 Some Gambling Games in Detail |
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161 | (16) |
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161 | (5) |
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The "Ultimate Winning Strategy" |
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166 | (3) |
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169 | (3) |
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The Gantt Chart and a Hint of Another Approach |
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172 | (2) |
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174 | (3) |
9 Scheduling and Waiting |
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177 | (10) |
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177 | (1) |
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Scheduling Appointments in the Doctor's Office |
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177 | (3) |
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180 | (2) |
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182 | (3) |
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185 | (2) |
10 Combined and Conditional Probabilities |
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187 | (12) |
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187 | (1) |
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Functional Notation (Again) |
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187 | (2) |
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189 | (3) |
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192 | (3) |
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The Shared Birthday Problem |
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195 | (2) |
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197 | (2) |
11 Bayesian Statistics |
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199 | (22) |
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199 | (3) |
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202 | (5) |
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Will Monty Hall Ever Go Away? |
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207 | (2) |
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209 | (1) |
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210 | (1) |
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211 | (3) |
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214 | (1) |
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215 | (2) |
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217 | (4) |
12 Estimation Problems |
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221 | (12) |
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The Number of Locomotives Problem |
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221 | (1) |
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Number of Locomotives, Improved Estimate |
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222 | (2) |
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224 | (3) |
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227 | (2) |
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229 | (3) |
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The Lighthouse Problem II |
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232 | (1) |
13 Two Paradoxes |
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233 | (14) |
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233 | (1) |
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233 | (3) |
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236 | (3) |
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239 | (1) |
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240 | (4) |
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244 | (3) |
14 Benford's Law |
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247 | (14) |
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247 | (1) |
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247 | (2) |
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249 | (3) |
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Surface Area of Countries of the World |
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252 | (1) |
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253 | (2) |
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255 | (4) |
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259 | (2) |
15 Networks, Infectious Diseases, and Chain Letters |
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261 | (16) |
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261 | (1) |
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261 | (4) |
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Propagation Along the Networks |
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265 | (5) |
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270 | (1) |
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271 | (2) |
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273 | (3) |
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276 | (1) |
16 Introduction to Frequentist Statistical Inference |
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277 | (26) |
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277 | (1) |
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277 | (3) |
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Sample Distributions and Standard Deviations |
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280 | (2) |
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Estimating Population Average from a Sample |
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282 | (3) |
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The Student-T Distribution |
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285 | (4) |
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Did a Sample Come from a Given Population? |
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289 | (1) |
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289 | (2) |
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Correlation and Causality |
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291 | (2) |
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293 | (1) |
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294 | (1) |
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295 | (3) |
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298 | (5) |
17 Statistical Mechanics and Thermodynamics |
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303 | (8) |
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303 | (1) |
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304 | (2) |
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(Concepts of) Thermodynamics |
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306 | (5) |
18 Chaos and Quanta |
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311 | (12) |
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311 | (1) |
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311 | (8) |
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Probability in Quantum Mechanics |
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319 | (4) |
Appendix |
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323 | (6) |
Index |
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329 | |