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동의어 포함

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1 Introduction and Overview 1

1.1 Making decisions under uncertainty 1

1.2 Overview of this book 3

2 Probability 9

2.1 Sample space, events, and probability 9

2.2 Rules of Probability 11

2.3 Equally likely outcomes. Combinatorics 20

2.4 Conditional probability. Independence 28

3 Discrete Random Variables and their Distributions 41

3.1 Distribution of a random variable 41

3.2 Distribution of a random vector 46

3.3 Expectation and variance 49

3.4 Families of discrete distributions 61

4 Continuous Distributions 81

4.1 Probability density 81

4.2 Families of continuous distributions 86

4.3 Central Limit Theorem 100

5 Computer Simulations and Monte Carlo Methods 111

5.1 Introduction 111

5.2 Simulation of random variables 114

5.3 Solving problems by Monte Carlo methods 126

6 Stochastic Processes 143

6.1 Definitions and Classifications 143

6.2 Markov processes and Markov chains 145

6.3 Counting processes 162

6.4 Simulation of stochastic processes 172

7 Queuing Systems 183

7.1Main components of a queuing system 183

7.2 The Little's Law 186

7.3 Bernoulli single-server queuing process 189

7.4 MIMl1 system 195

7.5 Multiserver queuing systems 202

7.6 Simulation of queuing systems 212

8 Introduction to Statistics 221

8.1Population and sample, parameters and statistics 222

8.2 Simple descriptive statistics 224

8.3 Graphical statistics 238

9 Statistical Inference 253

9.1Parameter estimation 253

9.2 Confidence intervals 262

9.3 Unknown standard deviation 270

9.4 Hypothesis testing 282

9.5 Bayesian estimation and hypothesis testing 305

10 Regression 327

10.1 Least squares estimation 327

10.2 Analysis of variance, prediction, and further inference 335

10.3 Multivariate regression 348

10.4 Model building 358

11 Appendix 371

11.1 Inventory of distributions 371

11.2 Distribution tables 377

11.3 Calculus review 391

11.4 Matrices and Linear systems 398

11.5 Answers to selected exercises 404

Index 409

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