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Chapter 1 Discrete Probability |
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1.1 The Cast of Characters |
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1 | (9) |
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1.2 Properties of Probability |
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10 | (13) |
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23 | (10) |
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33 | (15) |
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Sampling in Sequence without Replacement |
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34 | (4) |
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Sampling in a Batch without Replacement |
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38 | (4) |
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Other Sampling Situations |
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42 | (6) |
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1.5 Conditional Probability |
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48 | (14) |
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51 | (5) |
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56 | (6) |
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62 | (11) |
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Chapter 2 Discrete Distributions |
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2.1 Discrete Random Variables, Distributions, and Expectations |
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73 | (21) |
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Mean, Variance, and Other Moments |
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79 | (6) |
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Two Special Distributions |
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85 | (9) |
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2.2 Bernoulli and Binomial Random Variables |
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94 | (13) |
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102 | (5) |
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2.3 Geometric and Negative Binomial Random Variables |
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107 | (8) |
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115 | (9) |
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120 | (4) |
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2.5 Joint, Marginal, and Conditional Distributions |
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124 | (12) |
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136 | (23) |
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Covariance and Correlation |
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140 | (8) |
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148 | (11) |
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Chapter 3 Continuous Probability |
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3.1 From the Finite to the (Very) Infinite |
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159 | (12) |
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3.2 Continuous Random Variables and Distributions |
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171 | (21) |
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Joint, Marginal, and Conditional Distributions |
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178 | (14) |
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3.3 Continuous Expectation |
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192 | (15) |
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Chapter 4 Continuous Distributions |
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4.1 The Normal Distribution |
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207 | (18) |
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4.2 Bivariate Normal Distribution |
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225 | (21) |
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229 | (6) |
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Marginal and Conditional Distributions |
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235 | (11) |
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4.3 New Random Variables from Old |
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246 | (13) |
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C.D.F. Technique and Simulation |
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247 | (5) |
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Moment-Generating Functions |
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252 | (7) |
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259 | (14) |
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273 | (8) |
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273 | (4) |
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The Exponential Distribution |
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277 | (4) |
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4.6 Chi-Square, Student's t, and F-Distributions |
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281 | (19) |
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282 | (7) |
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289 | (4) |
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293 | (7) |
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4.7 Transformations of Normal Random Variables |
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300 | (13) |
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301 | (5) |
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Quadratic Forms in Normal Random Vectors |
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306 | (7) |
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Chapter 5 Asymptotic Theory |
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5.1 Strong and Weak Laws of Large Numbers |
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313 | (7) |
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5.2 Central Limit Theorem |
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320 | (9) |
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Chapter 6 Stochastic Processes and Applications |
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329 | (15) |
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331 | (3) |
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334 | (4) |
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338 | (6) |
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344 | (8) |
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352 | (13) |
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Long Run Distribution of System Size |
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353 | (5) |
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Waiting Time Distribution |
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358 | (1) |
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359 | (6) |
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365 | (14) |
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Geometric Brownian Motion |
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373 | (6) |
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6.5 Financial Mathematics |
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379 | (16) |
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380 | (5) |
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385 | (10) |
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A Introduction to Mathematica |
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395 | (28) |
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B Glossary of Mathematica Commands for Probability |
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423 | (8) |
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C Short Answers to Selected Exercises |
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431 | (14) |
| References |
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445 | (2) |
| Index |
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447 | |