商品簡介
作者簡介
Sheldon M. Ross 國際知名概率與統計學家，南加州大學工業工程與運籌系系主任。1968年博士畢業於斯坦福大學統計系，曾在加州大學伯克利分校任教多年。研究領域包括：隨機模型、仿真類比、統計分析、金融數學等。Ross教授著述頗豐，他的多種暢銷數學和統計教材均產生了世界性的影響，如《概率論基礎教程（第8版）》等。
目次
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 6
1.5 Independent Events 9
1.6 Bayes’ Formula 11
Exercises 14
References 19
2 Random Variables 21
2.1 Random Variables 21
2.2 Discrete Random Variables 25
2.2.1 The Bernoulli Random Variable 26
2.2.2 The Binomial Random Variable 26
2.2.3 The Geometric Random Variable 28
2.2.4 The Poisson Random Variable 29
2.3 Continuous Random Variables 30
2.3.1 The Uniform Random Variable 31
2.3.2 Exponential Random Variables 32
2.3.3 Gamma Random Variables 33
2.3.4 Normal Random Variables 33
2.4 Expectation of a Random Variable 34
2.4.1 The Discrete Case 34
2.4.2 The Continuous Case 37
2.4.3 Expectation of a Function of a Random Variable 38
2.5 Jointly Distributed Random Variables 42
2.5.1 Joint Distribution Functions 42
2.5.2 Independent Random Variables 45
2.5.3 Covariance and Variance of Sums of Random Variables 46
2.5.4 Joint Probability Distribution of Functions of Random Variables 55
2.6 Moment Generating Functions 58
2.6.1 The Joint Distribution of the Sample Mean and Sample Variance from a
2.7 The Distribution of the Number of Events that Occur 69
2.8 Limit Theorems 71
2.9 Stochastic Processes 77
Exercises 79
References 91
3 Conditional Probability and Conditional Expectation 93
3.1 Introduction 93
3.2 The Discrete Case 93
3.3 The Continuous Case 97
3.4 Computing Expectations by Conditioning 100
3.4.1 Computing Variances by Conditioning 111
3.5 Computing Probabilities by Conditioning 115
3.6 Some Applications 133
3.6.1 A List Model 133
3.6.2 A Random Graph 135
3.6.3 Uniform Priors, Polya’s Urn Model, and Bose—Einstein Statistics 141
3.6.4 Mean Time for Patterns 146
3.6.5 The k-Record Values of Discrete Random Variables 149
3.6.6 Left Skip Free Random Walks 152
3.7 An Identity for Compound Random Variables 157
3.7.1 Poisson Compounding Distribution 160
3.7.2 Binomial Compounding Distribution 161
3.7.3 A Compounding Distribution Related to the Negative Binomial 162
Exercises 163
4 Markov Chains 183
4.1 Introduction 183
4.2 Chapman–Kolmogorov Equations 187
4.3 Classification of States 194
4.4 Long-Run Proportions and Limiting Probabilities 204
4.4.1 Limiting Probabilities 219
4.5 Some Applications 220
4.5.1 The Gambler’s Ruin Problem 220
4.5.2 A Model for Algorithmic Efficiency 223
4.5.3 Using a Random Walk to Analyze a Probabilistic Algorithm for the Satisfiability Problem 226
4.6 Mean Time Spent in Transient States 231
4.7 Branching Processes 234
4.8 Time Reversible Markov Chains 237
4.9 Markov Chain
4.10 Markov Decision Processes 251
4.11 Hidden Markov Chains 254
4.11.1 Predicting the States 259
Exercises 261
References 275
5 The Exponential Distribution and the Poisson Process 277
5.1 Introduction 277
5.2 The Exponential Distribution 278
5.2.1 Definition 278
5.2.2 Properties of the Exponential Distribution 280
5.2.3 Further Properties of the Exponential Distribution 287
5.2.4 Convolutions of Exponential Random Variables 293
5.3 The Poisson Process 297
5.3.1 Counting Processes 297
5.3.2 Definition of the Poisson Process 298
5.3.3 Interarrival and Waiting Time Distributions 301
5.3.4 Further Properties of Poisson Processes 303
5.3.5 Conditional Distribution of the Arrival Times 309
5.3.6 Estimating Software Reliability 320
5.4 Generalizations of the Poisson Process 322
5.4.1 Nonhomogeneous Poisson Process 322
5.4.2 Compound Poisson Process 327
5.4.3 Conditional or Mixed Poisson Processes 332
5.5 Random Intensity Functions and Hawkes Processes 334
Exercises 338
References 356
6 Continuous-Time Markov Chains 357
6.1 Introduction 357
6.2 Continuous-Time Markov Chains 358
6.3 Birth and Death Processes 359
6.4 The Transition Probability Function Pij(t) 366
6.5 Limiting Probabilities 374
6.6 Time Reversibility 380
6.7 The Reversed Chai
您曾經瀏覽過的商品
購物須知
大陸出版品因裝訂品質及貨運條件與台灣出版品落差甚大，除封面破損、內頁脫落等較嚴重的狀態，其餘商品將正常出貨。
特別提醒：部分書籍附贈之內容(如音頻mp3或影片dvd等)已無實體光碟提供，需以QR CODE 連結至當地網站註冊“並通過驗證程序”，方可下載使用。
無現貨庫存之簡體書，將向海外調貨：
海外有庫存之書籍，等候約45個工作天;
海外無庫存之書籍，平均作業時間約60個工作天，然不保證確定可調到貨，尚請見諒。
為了保護您的權益，「三民網路書店」提供會員七日商品鑑賞期(收到商品為起始日)。
若要辦理退貨，請在商品鑑賞期內寄回，且商品必須是全新狀態與完整包裝(商品、附件、發票、隨貨贈品等)否則恕不接受退貨。