概率论基础教程(英文版 第7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7版)

Sheldon M.Ross (作者)
终止销售
本书是全球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。
本书作为概率论的入门书,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,也可供概率应用工作者参考.
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出版信息

  • 书  名概率论基础教程(英文版 第7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2007-08-30
  • 书  号978-7-115-16541-1
  • 定  价69.00 元
  • 页  数576
  • 开  本16开
  • 出版状态终止销售
  • 原书名A First Course in Probability
  • 原书号0-13-185662-6

同系列书

目录

Preface
1 Combinatorial Analysis 1
1.1 Introduction 1
1.2 The Basic Principle of Counting 2
1.3 Permutations3
1.4 Combinations6
1.5 Multinomial Coefficients 10
1.6 The Number of Integer Solutions of Equations* 12
Summary 15
Problems 16
Theoretical Exercises 19
Self-Test Problems and Exercises 22
2 Axioms of Probability 24
2.1 Introduction 24
2.2 Sample Space and Events 24
2.3 Axioms of Probability 29
2.4 Some Simple Propositions 31
2.5 Sample Spaces Having Equally Likely Outcomes 37
2.6 Probability as a Continuous Set Function* 49
2.7 Probability as a Measure of Belief 53
Summary 54
Problems 55
Theoretical Exercises 61
Self-Test Problems and Exercises 63
3 Conditional Probability and Independence 66
3.1 Introduction 66
3.2 Conditional Probabilities 66
3.3 Bayes' Formula 72
3.4 Independent Events 87
3.5 P (.|F) Is a Probability 101
Summary 110
Problems 111
Theoretical Exercises 124
Self-Test Problems and Exercises 128
4 Random Variables 132
4.1 Random Variables 132
4.2 Discrete Random Variables 138
4.3 Expected Value 140
4.4 Expectation of a Function of a Random Variable 144
4.5 Variance148
4.6 The Bernoulli and Binomial Random Variables 150
4.6.1 Properties of Binomial Random Variables 155
4.6.2 Computing the Binomial Distribution Function 158
4.7 The Poisson Random Variable 160
4.7.1 Computing the Poisson Distribution Function 173
4.8 Other Discrete Probability Distributions 173
4.8.1 The Geometric Random Variable 173
4.8.2 The Negative Binomial Random Variable 175
4.8.3 The Hypergeometric Random Variable 178
4.8.4 The Zeta (or Zipf) Distribution 182
4.9 Properties of the Cumulative Distribution Function 183
Summary 185
Problems 187
Theoretical Exercises 1.97
Self-Test Problems and Exercises 201
5 Continuous Random Variables 205
5.1 Introduction 205
5.2 Expectation and Variance of Continuous Random Variables 209
5.3 The Uniform Random Variable 214
5.4 Normal Random Variables 218
5.4.1 The Normal Approximation to the Binomial Distribution 225
5.5 Exponential Random Variables 230
5.5.1 Hazard Rate Functions 234
5.6 Other Continuous Distributions 237
5.6.1 The Gamma Distribution 237
5.6.2 The Weibull Distribution 239
5.6.3 The Cauchy Distribution 239
5.6.4 The Beta Distribution 240
5.7 The Distribution of a Function of a Random Variable 242
Summary 244
Problems 247
Theoretical Exercises 251
Self-Test Problems and Exercises 254
6 Jointly Distributed Random Variables 258
6.1 Joint Distribution Functions 258
6.2 Independent Random Variables 267
6.3 Sums of Independent Random Variables 280
6.4 Conditional Distributions: Discrete Case 288
6.5 Conditional Distributions: Continuous Case 291
6.6 Order Statistics* 296
6.7 Joint Probability Distribution of Functions of Random Variables 300
6.8 Exchangeable Random Variables* 308
Summary311
Problems 313
Theoretical Exercises 319
Self-Test Problems and Exercises 323
7 Properties of Expectation 327
7.1 Introduction 327
7.2 Expectation of Sums of Random Variables 328
7.2.1 Obtaining Bounds from Expectations via the Probabilistic Method* 342
7.2.2 The Maximum-Minimums Identity* 344
7.3 Moments of the Number of Events that Occur 347
7.4 Covariance, Variance of Sums, and Correlations 355
7.5 Conditional Expectation 365
7.5.1 Definitions 365
7.5.2 Computing Expectations by Conditioning 367
7.5.3 Computing Probabilities by Conditioning 376
7.5.4 Conditional Variance 380
7.6 Conditional Expectation and Prediction 382
7.7 Moment Generating Functions 387
7.7.1 Joint Moment Generating Functions 397
7.8 Additional Properties of Normal Random Variables 399
7.8.1 The Multivariate Normal Distribution 399
7.8.2 The Joint Distribution of the Sample Mean and Sample Variance 402
7.9 General Definition of Expectation 404
Summary 405
Problems 408
Theoretical Exercises 418
Self-Test Problems and Exercises 426
8 Limit Theorems 430
8.1 Introduction 430
8.2 Chebyshev's Inequality and the Weak Law of Large Numbers 430
8.3 The Central Limit Theorem 434
8.4 The Strong Law of Large Numbers 443
8.5 Other Inequalities AA5
8.6 Bounding The Error Probability 454
Summary 456
Problems 457
Theoretical Exercises 459
Self-Test Problems and Exercises 461
9 Additional Topics in Probability 463
9.1 The Poisson Process 463
9.2 Markov Chains 466
9.3 Surprise, Uncertainty, and Entropy 472
9.4 Coding Theory and Entropy 476
Summary 483
Theoretical Exercises 484
Self-Test Problems and Exercises 485
10 Simulation 487
10.1 Introduction487
10.2 General Techniques for Simulating Continuous Random Variables 490
10.2.1 The Inverse Transformation Method 490
10.2.2 The Rejection Method 491
10.3 Simulating from Discrete Distributions 497
10.4 Variance Reduction Techniques 499
10.4.1 Use of Antithetic Variables 500
10.4.2 Variance Reduction by Conditioning 501
10.4.3 Control Variates 503
Summary 503
Problems 504
Self-Test Problems and Exercises 506
APPENDICES
A Answers to Selected Problems 508
B Solutions to Self-Test Problems and Exercises 511
Index 561
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