Introduction to Probability Models （Ninth Edition）经典名著 原版高清 非扫描

1. Introduction to Probability Theory 1
1.1. Introduction 1
1.2. Sample Space and Events 1
1.3. Probabilities Defined on Events 4
1.4. Conditional Probabilities 7
1.5. Independent Events 10
1.6. Bayes’ Formula 12
Exercises 15
References 21
2. Random Variables 23
2.1. Random Variables 23
2.2. Discrete Random Variables 27
2.2.1. The Bernoulli Random Variable 28
2.2.2. The Binomial Random Variable 29
2.2.3. The Geometric Random Variable 31
2.2.4. The Poisson Random Variable 32
2.3. Continuous Random Variables 34
2.3.1. The Uniform Random Variable 35
2.3.2. Exponential Random Variables 36
2.3.3. Gamma Random Variables 37
2.4. Expectation of a Random Variable 38
2.4.1. The Discrete Case 38
2.4.2. The Continuous Case 41
2.4.3. Expectation of a Function of a Random Variable 43
2.5. Jointly Distributed Random Variables 47
2.5.1. Joint Distribution Functions 47
2.5.2. Independent Random Variables 51
2.5.3. Covariance and Variance of Sums of Random Variables 53
2.5.4. Joint Probability Distribution of Functions of Random
Variables 61
2.6. Moment Generating Functions 64
2.6.1. The Joint Distribution of the Sample Mean and Sample
Variance from a Normal Population 74
2.7. Limit Theorems 77
2.8. Stochastic Processes 83
Exercises 85
References 96
3. Conditional Probability and Conditional
Expectation 97
3.1. Introduction 97
3.2. The Discrete Case 97
3.3. The Continuous Case 102
3.4. Computing Expectations by Conditioning 105
3.4.1. Computing Variances by Conditioning 117
3.5. Computing Probabilities by Conditioning 120
3.6. Some Applications 137
3.6.1. A List Model 137
3.6.2. A Random Graph 139
3.6.3. Uniform Priors, Polya’s Urn Model, and
Bose–Einstein Statistics 147
3.6.4. Mean Time for Patterns 151
3.6.5. The k-Record Values of Discrete Random Variables 155
3.7. An Identity for Compound Random Variables 158
3.7.1. Poisson Compounding Distribution 161
3.7.2. Binomial Compounding Distribution 163
3.7.3. A Compounding Distribution Related to the Negative
Binomial 164
Exercises 1652.3.4. Normal Random Variables 37

4. Markov Chains 185
4.1. Introduction 185
4.2. Chapman–Kolmogorov Equations 189
4.3. Classification of States 193
4.4. Limiting Probabilities 204
4.5. Some Applications 217
4.5.1. The Gambler’s Ruin Problem 217
4.5.2. A Model for Algorithmic Efficiency 221
4.5.3. Using a Random Walk to Analyze a Probabilistic Algorithm
for the Satisfiability Problem 224
4.6. Mean Time Spent in Transient States 230
4.7. Branching Processes 233
4.8. Time Reversible Markov Chains 236
4.9. Markov Chain Monte Carlo Methods 247
4.10. Markov Decision Processes 252
4.11. Hidden Markov Chains 256
4.11.1. Predicting the States 261
Exercises 263
References 280
5. The Exponential Distribution and the Poisson
Process 281
5.1. Introduction 281
5.2. The Exponential Distribution 282
5.2.1. Definition 282
5.2.2. Properties of the Exponential Distribution 284
5.2.3. Further Properties of the Exponential Distribution 291
5.2.4. Convolutions of Exponential Random Variables 298
5.3. The Poisson Process 302
5.3.1. Counting Processes 302
5.3.2. Definition of the Poisson Process 304
5.3.3. Interarrival and Waiting Time Distributions 307
5.3.4. Further Properties of Poisson Processes 310
5.3.5. Conditional Distribution of the Arrival Times 316
5.3.6. Estimating Software Reliability 328
5.4. Generalizations of the Poisson Process 330
5.4.1. Nonhomogeneous Poisson Process 330
5.4.2. Compound Poisson Process 337
5.4.3. Conditional or Mixed Poisson Processes 343

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