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1 Introduction and Overview |
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1 | |
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1.1 Making decisions under uncertainty |
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1 | |
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1.2 Overview of this book |
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3 | |
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9 | |
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2.1 Sample space, events, and probability |
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9 | |
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11 | |
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2.3 Equally likely outcomes. Combinatorics |
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20 | |
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2.4 Conditional probability. Independence |
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28 | |
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3 Discrete Random Variables and their Distributions |
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41 | |
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3.1 Distribution of a random variable |
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41 | |
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3.2 Distribution of a random vector |
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46 | |
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3.3 Expectation and variance |
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49 | |
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3.4 Families of discrete distributions |
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61 | |
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4 Continuous Distributions |
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81 | |
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81 | |
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4.2 Families of continuous distributions |
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86 | |
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4.3 Central Limit Theorem |
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100 | |
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5 Computer Simulations and Monte Carlo Methods |
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111 | |
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111 | |
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5.2 Simulation of random variables |
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114 | |
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5.3 Solving problems by Monte Carlo methods |
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126 | |
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143 | |
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6.1 Definitions and Classifications |
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143 | |
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6.2 Markov processes and Markov chains |
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145 | |
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162 | |
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6.4 Simulation of stochastic processes |
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172 | |
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183 | |
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7.1 Main components of a queuing system |
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183 | |
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186 | |
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7.3 Bernoulli single-server queuing process |
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189 | |
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195 | |
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7.5 Multiserver queuing systems |
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202 | |
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7.6 Simulation of queuing systems |
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212 | |
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8 Introduction to Statistics |
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221 | |
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8.1 Population and sample, parameters and statistics |
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222 | |
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8.2 Simple descriptive statistics |
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224 | |
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238 | |
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253 | |
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253 | |
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262 | |
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9.3 Unknown standard deviation |
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270 | |
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282 | |
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9.5 Bayesian estimation and hypothesis testing |
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305 | |
| 10 Regression |
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327 | |
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10.1 Least squares estimation |
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327 | |
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10.2 Analysis of variance, prediction, and further inference |
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335 | |
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10.3 Multivariate regression |
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348 | |
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358 | |
| 11 Appendix |
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371 | |
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11.1 Inventory of distributions |
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371 | |
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377 | |
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391 | |
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11.4 Matrices and linear systems |
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398 | |
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11.5 Answers to selected exercises |
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404 | |
| Index |
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409 | |
