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Original edition, entitled PROBABILITY AND STATISTICS, 4E, 9780321500465 by DEGROOT, MORRIS H.; SCHERVISH, MARK J., published by Pearson Education, Inc, publishing as Pearson, Copyright 2012, 2002.

All rights reserved. No part of this book may be re

1 introduction to probability 1

1.1 the history of probability 1

1.2 interpretations of probability 2

1.3 experiments and events 5

1.4 set theory 6

1.5 the definition of probability 16

1.6 finite sample spaces 22

1.7 counting methods 25

1.8 combinatorial methods 32

1.9 multinomial coefficients 42

1.10 the probability of a union of events 46

1.11 statistical swindles 51

1.12 supplementary exercises 53

2 conditional probability 55

2.1 the definition of conditional probability 55

2.2 independent events 66

2.3 bayes’ theorem 76

2.4 the gambler’s ruin problem 86

2.5 supplementary exercises 90

3 random variables and distributions 93

3.1 random variables and discrete distributions 93

3.2 continuous distributions 100

3.3 the cumulative distribution function 107

3.4 bivariate distributions 118

3.5 marginal distributions 130

3.6 conditional distributions 141

3.7 multivariate distributions 152

3.8 functions of a random variable 167

3.9 functions of two or more random variables 175

3.10 markov chains 188

3.11 supplementary exercises 202

4 expectation 207

4.1 the expectation of a random variable 207

4.2 properties of expectations 217

4.3 variance 225

4.4 moments 234

4.5 the mean and the median 241

4.6 covariance and correlation 248

4.7 conditional expectation 256

4.8 utility 265

4.9 supplementary exercises 272

5 spe distributions 275

5.1 introduction 275

5.2 the bernoulli and binomial distributions 275

5.3 the hypergeometric distributions 281

5.4 the poisson distributions 287

5.5 the negative binomial distributions 297

5.6 the normal distributions 302

5.7 the gamma distributions 316

5.8 the beta distributions 327

5.9 the multinomial distributions 333

5.10 the bivariate normal distributions 337

5.11 supplementary exercises 345

6 large random samples 347

6.1 introduction 347

6.2 the law of large numbers 348

6.3 the central limit theorem 360

6.4 the correction for continuity 371

6.5 supplementary exercises 375

7 estimation 376

7.1 statistical inference 376

7.2 prior and posterior distributions 385

7.3 conjugate prior distributions 394

7.4 bayes estimators 408

7.5 maximum likelihood estimators 417

7.6 properties of maximum likelihood estimators 426

7.7 sufficient statistics 443

7.8 jointly sufficient statistics 449

7.9 improving an estimator 455

7.10 supplementary exercises 461

8 sampling distributions of estimators 464

8.1 the sampling distribution of a statistic 464

8.2 the chi-square distributions 469

8.3 joint distribution of the sample mean and sample variance 473

8.4 the t distributions 480

8.5 confidence intervals 485

8.6 bayesian analysis of samples from a normal distribution 495

8.7 unbiased estimators 506

8.8 fisher information 514

8.9 supplementary exercises 528

9 testing hypotheses 530

9.1 problems of testing hypotheses 530

9.2 testing simple hypotheses 550

9.3 uniformly most powerful tests 559

9.4 two-sided alternatives 567

9.5 the t test 576

9.6 comparing the means of two normal distributions 587

9.7 the f distributions 597

9.8 bayes test procedures 605

9.9 foundational issues 617

9.10 supplementary exercises 621

10 categorical data and nonparametric methods 624

10.1 tests of goodness-of-fit 624

10.2 goodness-of-fit for composite hypotheses 633

10.3 contingency tables 641

10.4 tests of homogeneity 647

10.5 simpson’s paradox 653

10.6 kolmogorov-smirnov tests 657

10.7 robust estimation 666

10.8 sign and rank tests 678

10.9 supplementary exercises 686

11 linear statistical models 689

11.1 the method of least squares 689

11.2 regression 698

11.3 statistical inference in simple linear regression 707

11.4 bayesian inference in simple linear regression 729

11.5 the general linear model and multiple regression 736

11.6 analysis of variance 754

11.7 the two-way layout 763

11.8 the two-way layout with replications 772

11.9 supplementary exercises 783

12 simulation 787

12.1 what is simulation? 787

12.2 why is simulation useful? 791

12.3 simulating specific distributions 804

12.4 importance sampling 816

12.5 markov chain monte carlo 823

12.6 the bootstrap 839

12.7 supplementary exercises 850

tables 853

answers to odd-numbered exercises 865

references 879

index 885

Morris H. DeGroot(1931–1989) 世界著名的统计学家。生前曾任国际统计学会、美国科学促进会、统计学会、数理统计学会、计量经济学会会士。卡内基梅隆大学教授，1957年加入该校，1966年创办该校统计系。DeGroot在学术上异常活跃和多产，曾发表一百多篇论文，还著有 Optimal Statistical Decisions和 Statistics and the Law。为纪念他的著作对统计教学的贡献，国际贝叶斯分析学会特别设立了DeGroot奖表彰优秀统计学著作。

Mark J. Schervish 世界著名的统计学家，美国统计学会、数理统计学会会士。于1979年获得伊利诺大学的博士学位，之后就在卡内基梅隆大学统计系工作，教授数学、概率、统计和计算金融等课程，现为该系系主任。Schervish在学术上非常活跃，成果颇丰，还因在统计推断和贝叶斯统计方面的基石性工作而闻名，除本书外，他还著有Theory of Statistics和 Rethinking the Foundations of Statistics。

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we will use set theory for the mathematical model of events.outcomes of an experiment are elements of some sample space S,and each event is a subset of S.two events both occur if the outcome is in the intersection of two sets.at least one of a collection of events occurs if the outcome is the union of the sets.two events can not both occur if the sets are disjoint.an event fails to occur if the outcome is the complement of the set.the empty set stands for every event that cannot possibly occur.the collection of events is assumed to contain the sample space,the complement of each event,and the union of each countable collection of events.

a box contains 100 balls,of which r are red.suppose that the balls are drawn from the box one at a time,at random,without replacement.determine(a) the probability that the first ball drawn will be red;(b)the probability that the 50th ball drawn will be red;(c)the prbability that the last ball drawn will be red.

9.if n people are seated in a random manner in a row containing 2n seats,what is the probability that no people will occupy adjacent seats?

Let Pn be the proportion of patients who don’t relapse out of the first n. It can be shown that the probability is 1 that Pn converges to something as n → ∞. That something can be thought of as P , which we have been calling the proportion of successes in a very large population. In this sense, P is a ran- dom variable because it is a function of other random variables.

Suppose that the number of potential patients is enough larger than any sam- ple that we will see to make the approximation in Theorem 5.3.4 applicable. Then P is just the proportion of successes among the large population of potential pa- tients. Conditional on P = p, the number of successes in a sample of n patients will be approximately a binomial random variable with paramters n and p according to Theorem 5.3.4. If the outcomes of the patients in the sample are random variables, then it makes sense that the proportion of successes among those patients is also random.

The interesting probabilistic properties of δ can be summarized by computing, for each value of θ∈Ω, either the probability π(θ|δ) that the test δ will reject H₀....

书籍介绍

这本经典的概率论与数理统计教材，多年来畅销不衰，被很多名校采用，包括卡内基梅隆大学、哈佛大学、麻省理工学院、华盛顿大学、芝加哥大学、康乃尔大学、杜克大学、加州大学洛杉矶分校等。

本书包括概率论、数理统计两部分，内容丰富完整，适当地选择某些章节，可以作为一学年的概率论与数理统计课程的教材，亦可作为一学期的概率论与随机过程的教材。适合数学、统计学、经济学等专业高年级本科生和研究生用，也可供统计工作人员用作参考书。

本书主要特点

 叙述清晰易懂，内容深入浅出。作者用大量颇具启发性的例子引入论题、阐释理论和证明。例题涉及面广，除了那些解释基本概念的一些著名例题外，还有很多新颖的例题，描述了概率论在遗传学、排队论、计算金融学和计算机科学中的应用。

 内容取材比较时尚新颖。新版不但重写了很多章节，还介绍了在计算机科学中日益重要的Chernoff界，以及矩方法、Newton法、EM算法、枢轴量、似然比检验的大样本分布等方面的知识，将目前研究前沿的一些问题深入浅出地融人教材。

 为授课教师免费提供教师解答手册（Instructor’s Solutions Manual）。书后还提供了奇数号习题的答案。