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Book Categories |
Chapter 1 | Discrete Probability | |
1.1 | The Cast of Characters | 1 |
1.2 | Properties of Probability | 10 |
1.3 | Simulation | 25 |
1.4 | Random Sampling | 38 |
Sampling in Sequence without Replacement | 38 | |
Sampling in a Batch without Replacement | 42 | |
Other Sampling Situations | 48 | |
1.5 | Conditional Probability | 54 |
Multiplication Rules | 56 | |
Bayes' Formula | 61 | |
1.6 | Independence | 67 |
Chapter 2 | Discrete Distributions | |
2.1 | Discrete Random Variables, Distributions, and Expectations | 79 |
Mean, Variance, and Other Moments | 86 | |
Two Special Distributions | 91 | |
2.2 | Bernoulli and Binomial Random Variables | 101 |
2.3 | Geometric and Negative Binomial Random Variables | 110 |
2.4 | Poisson Distribution | 119 |
Poisson Processes | 124 | |
2.5 | Joint, Marginal, and Conditional Distributions | 129 |
2.6 | More on Expectation | 146 |
Chapter 3 | Continuous Probability | |
3.1 | From the Finite to the (Very) Infinite | 163 |
3.2 | Continuous Random Variables and Distributions | 171 |
Joint, Marginal, and Conditional Distributions | 179 | |
3.3 | Continuous Expectation | 194 |
Chapter 4 | Continuous Distributions | |
4.1 | The Normal Distribution | 209 |
4.2 | Bivariate Normal Distribution | 225 |
Bivariate Normal Density | 227 | |
Marginal and Conditional Distributions | 233 | |
4.3 | New Random Variables from Old | 245 |
C.D.F. Technique and Simulation | 246 | |
Moment-Generating Functions | 252 | |
4.4 | Gamma Distributions | 259 |
Main Properties | 259 | |
The Exponential Distribution | 264 | |
More on the Poisson Process | 267 | |
4.5 | Chi-Square, Student's t, and F-distributions | 272 |
Chi-Square Distribution | 272 | |
Student's t-Distribution | 279 | |
F-Distribution | 283 | |
Chapter 5 | Asymptotic Theory | |
5.1 | Strong and Weak Laws of Large Numbers | 293 |
5.2 | Central Limit Theorem | 301 |
Chapter 6 | Applications of Probability | |
6.1 | Markov Chains | 309 |
6.2 | Queues | 320 |
Long-Run Distribution of System Size | 322 | |
Waiting Time Distribution | 327 | |
Simulating Queues | 328 | |
6.3 | Mathematical Finance | 336 |
Optimal Portfolios | 336 | |
Option Pricing | 341 | |
Appendix | ||
A. | Short Answers to Selected Exercises | 353 |
B. | Glossary of Mathematica Commands for Probability | 365 |
References | 373 | |
Index | 375 |
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