概率论基础教程(英文版 第8版)
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图灵原版数学统计学系列

概率论基础教程(英文版 第8版)

终止销售
本书是世界各国高校广泛采用的概率论教材,通过大量的例子讲述了概率论的基础知识,主要内容有组合分析、概率论公理化、条件概率和独立性、离散和连续型随机变量、随机变量的联合分布、期望的性质、极限定理等.本书附有大量的练习,分为习题、理论习题和自检习题三大类,其中自检习题部分还给出全部解答.
本书适用于大专院校数学、统计、工程和相关专业(包括计算科学、生物、社会科学和管理科学)的学生阅读,也可供各学科专业科技人员参考.
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出版信息

  • 书  名概率论基础教程(英文版 第8版)
  • 系列书名图灵原版数学统计学系列
  • 执行编辑关于本书的内容有任何问题,请联系 傅志红
  • 出版日期2009-07-10
  • 书  号978-7-115-20954-2
  • 定  价69.00 元
  • 页  数544
  • 开  本16开
  • 出版状态终止销售
  • 原书名A First Course in Probability
  • 原书号978-0-13-603313-4

同系列书

目录

Preface xi
1 Combinatorial Analysis 1
1.1 Introduction 1
1.2 The Basic Principle of Counting 1
1.3 Permutations 3
1.4 Combinations 5
1.5 Multinomial Coefficients 9
1.6 The Number of Integer Solutlons of Equations 12
Summary 15
Problems 16
Theoretical Exercises 18
Self-Test Problems and Exercises 20
2 Axioms of Probability 22
2.1 Introduction 22
2.2 Sample Space and Events 22
2.3 Axioms of Probability 26
2.4 Some Simple Propositions 29
2.5 Sample Space Having Equally Likely Outcomes 33
2.6 Probability as a Continuous Set Function 44
2.7 Probability as a Measure of Belief 48
Summary 49
Problems 50
Theoretical Exercises 54
Self-Test Problems and Exercises 56
3 Conditional Probability and Independence 58
3.1 Introduction 58ts
3.2 Conditional Probalgllltle 58
3.3 Bayes's Formula 65
3.4 lnoependent Events 79
3.5 P(·|F) Is a Probability 93
Summary 101
Problems 102
Theoretical Exercises 110
Self-Test Problems and Exercises 114
4 Random Variables 117
4.1 Random Variables 117
4.2 Discrete Random Variables123
4.3 Expected Value 125
4.4 Expectation of a Function of a Random Variable 128
4.5 Variance 132
4.6 The Bernoulh and Binomial Random Variables 134
4.6.1 Properties of Binomial Random Variables 139
4.6.2 Computing the Binomial Distribution Function 142
4.7 The Poisson Random Variable .143
4.7.1 Computing the Poisson Distribution Function 154
4.8 Other Discrete Probability Distributions 155
4.8.1 The Geometric Random Variable 155
4.8.2 The Negative Binomial Random Variable 157
4.8.3 The Hypergeometric Random Variable 160
4.8.4 The Zeta (or Zipf) Distribution 163
4.9 Expected Value of Sums of Random Variables 164
4.10 Properties of the Cumulative Distribution Function 168
Summary 170
Problems 172
Theoretical Exercises 179
Self-Test Problems and Exercises183
5 Continuous Random Variables 186
5 1 Introduction 186
5.2 Expectation and Variance of Continuous Random Variables 190
5.3 The Uniform Random Variable 194
5.4 Normal Random Variables 198
5.4.1 The Normal Approximation to the Binomial Distribution 204
.5 Exponential Random Variables 208
5.5.1 Hazard Rate Functions .212
5.6 Other Continuous Distributions 215
5.6.1 The Gamma Dlstrlbutlon 215
5.6.2 The Weibull DlStrlbutlon 216
5.6.3 The-Cauchy Distribution 217
.6.4 The Beta DlStrlbutlon 218
5.7 The Distribution of a Function of a Random Variable 219
Summary 222
Problems 224
Theoretical Exercises227
Self-Test Problems and Exercises229
6 Jointly Distributed Random Variables232
6.1 Joint Distribution Functions 232
6.2 Independent Random Variables240
6.3 Sums of Independent Random Variables 252
6.3.1 Identically Distributed Uniform Random Variables 252
6.3.2 Gamma Random Variables 254
6.3.3 Normal Random Variables 256
6.3.4 Polsson and Binomial Random Variables 259
6 3 5 Geometric Random Variables 260
6.4 Conditional Distribution:Discrete Case 263
6.5 Conditional Distribution:Continuous Case 266
6 6 Order Statistics 270
6.7 Joint Probability Distribution of Functions of Random Variables 274
6.8 Exciaanzeaole Random Variables 282
Summary 285
Problems 287
Theoretical Exercises291
elf Test Problems and Exercises 293
7 Properties of Expectation 29")
7.1 Introduction 297
7.2 Expectation of Sums of Random Variabl via the Probabilistic Method 311
7.2.2 The Maximum-Minimums Identity 313
7.3 Moments of the Number of Events that Occur 315
7.4 Covariance, Variance of Sums, and Correlations 322
7.5 ConditionalExpectation 331
7.5.1 Definitions 331
7.5.2 Computing Expectations by Conditioning 333
7.5.3 Computing Probabilities by Conditioning 344
7.5.4 ConditionalVariance 347
7.6 Conditional Expectation and Prediction 349
7.7 Moment Generating Functions 354
7.7.1 Joint Moment Generating Functions 363
7.8 Addltlona proprietaries of Normal Random Variables 365
7.8.1 The Multivariate Normal Dlstrlbution 365
7.8.2 The Joint Distribution of the Sample Mean and Sample Variance 367
7.9 General Definition of Expectation369
Summary 37(3
Problems 373
Theoretical Exercises 38C
Self-Test Problems and Exercises38d
8 Limit Theorems 388
8.1 Introduction 388
8.2 Chebyshev's Inequality and the Weak Law of Large Numbers 388
8.3 The Central Limit Theorem 391
8.4 The Strong Law of Large Numbers 40C
8.5 Other Inequamles 403
8.6 Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson Random Variable 410
Summary 412
Problems 412
Theoretical Exercises 414
Self-Test Problems and Exercises 415
9 Additional Topics in Probability 417
9.1 The Poisson Process 417
9.2 Markov Chains 419
9.3 Surprise,Uncertainty, and Entropy 425
9.4 Coding Theory and Entropy 428
Summary 434
Problems and Theoretical Exercises 435
Self-Test Problems and Exercises436
References 436
10 Simulation 438
10.1 Introduction 438
10.2 General Techniques for Simulating Continuous Random Variables 440
10.2.1 The Inverse Transformation Method 441
10.2.2 The Rejection Method 442
10.3 Simulating from Discrete Distributions 447
10.4Variance Reduction Techniques 449
10.4.1 Use of Antithetic Variables 450
10.4.2 Variance Reduction by Conditioning 451
10.4.3 Control Variates 452
Summary 453
Problems 453
Self-Test Problems and Exercises 455
Reference 455
Answers to Selected Problems 457
Solutions to Self-Test Problems and Exercises 461
Index 521
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