概率論基礎(chǔ)教程（英文版·第9版）

前　言
第1章　組合分析1
1.1　引言1
1.2　計(jì)數(shù)基本法則2
1.3　排列3
1.4　組合5
1.5　多項(xiàng)式系數(shù)9
1.6　方程的整數(shù)解個(gè)數(shù)12
第2章　概率論公理21
2.1　引言21
2.2　樣本空間和事件21
2.3　概率論公理25
2.4　幾個(gè)簡(jiǎn)單命題28
2.5　等可能結(jié)果的樣本空間32
*2.6　概率：連續(xù)集函數(shù)42
2.7　概率：確信程度的度量46
第3章　條件概率和獨(dú)立性56
3.1　引言56
3.2　條件概率56
3.3　貝葉斯公式62
3.4　獨(dú)立事件75
3.5　P（·|F）是概率89
第4章　隨機(jī)變量112
4.1　隨機(jī)變量112
4.2　離散型隨機(jī)變量116
4.3　期望119
4.4　隨機(jī)變量函數(shù)的期望121
4.5　方差125
4.6　伯努利隨機(jī)變量和二項(xiàng)隨機(jī)變量127
4.7　泊松隨機(jī)變量135
4.8　其他離散型概率分布147
4.9　隨機(jī)變量和的期望155
4.10　分布函數(shù)的性質(zhì)159
第5章　連續(xù)型隨機(jī)變量176
5.1　引言176
5.2　連續(xù)型隨機(jī)變量的期望和方差179
5.3　均勻隨機(jī)變量184
5.4　正態(tài)隨機(jī)變量187
5.5　指數(shù)隨機(jī)變量197
5.6　其他連續(xù)型概率分布203
5.7　隨機(jī)變量函數(shù)的分布208
第6章　隨機(jī)變量的聯(lián)合分布220
6.1　聯(lián)合分布函數(shù)220
6.2　獨(dú)立隨機(jī)變量228
6.3　獨(dú)立隨機(jī)變量的和239
6.4　離散情形下的條件分布248
6.5　連續(xù)情形下的條件分布250
*6.6　次序統(tǒng)計(jì)量256
6.7　隨機(jī)變量函數(shù)的聯(lián)合分布260
*6.8　可交換隨機(jī)變量267
第7章　期望的性質(zhì)280
7.1　引言280
7.2　隨機(jī)變量和的期望281
7.3　試驗(yàn)序列中事件發(fā)生次數(shù)的矩298
7.4　隨機(jī)變量和的協(xié)方差、方差及相關(guān)系數(shù)304
7.5　條件期望313
7.6　條件期望及預(yù)測(cè)330
7.7　矩母函數(shù)334
7.8　正態(tài)隨機(jī)變量的更多性質(zhì)345
7.9　期望的一般定義349
第8章　極限定理367
8.1　引言367
8.2　切比雪夫不等式及弱大數(shù)定律367
8.3　中心極限定理370
8.4　強(qiáng)大數(shù)定律378
8.5　其他不等式382
8.6　用泊松隨機(jī)變量逼近獨(dú)立的伯努利隨機(jī)變量和的概率誤差界388
第9章　概率論的其他課題395
9.1　泊松過(guò)程395
9.2　馬爾可夫鏈397
9.3　驚奇、不確定性及熵402
9.4　編碼定理及熵405
第10章　模擬415
10.1　引言415
10.2　模擬連續(xù)型隨機(jī)變量的一般方法417
10.3　模擬離散分布424
10.4　方差縮減技術(shù)426
附錄A　部分習(xí)題答案433
附錄B　自檢習(xí)題解答435


Contents

Preface ix
1 Combinatorial Analysis1
1.1Introduction 1
1.2The Basic Principle of Counting2
1.3Permutations 3
1.4Combinations 5
1.5Multinomial Coefficients 9
1.6The Number of Integer Solutions of Equations12
2 Axioms of Probability 21
2.1Introduction 21
2.2Sample Spaceand Events21
2.3Axioms of Probability 25
2.4Some Simple Propositions 28
2.5Sample Spaces Having Equally Likely Outcomes32
2.6Probability as a Continuous Set Function 42
2.7Probability as a Measure of Belief 46
3Conditional Probability and Independence56
3.1Introduction 56
3.2Conditional Probabilities 56
3.3 Bayes’s Formula62
3.4 Independent Events 75
3.5 P(·|F)Isa Probability89
4 Random Variables 112
4.1Random Variables112
4.2Discrete Random Variables116
4.3Expected Value 119
4.4Expectation of a Function of a Random Variable121
4.5Variance 125
4.6The Bernoulli and Binomial Random Variables127
4.7The Poisson Random Variable135
4.8Other Discrete Probability Distributions 147
4.9Expected Value of Sums of Random Variables155
4.10Properties of the Cumulative Distribution Function159
5Continuous Random Variables 176
5.1Introduction 176
5.2Expectation and Variance of Continuous Random Variables179
5.3The Uniform Random Variable184
5.4Normal Random Variables187
5.5Exponential Random Variables197
5.6Other Continuous Distributions203
5.7The Distribution of a Function of a Random Variable208
6Jointly Distributed Random Variables220
6.1Joint Distribution Functions220
6.2Independent Random Variables228
6.3Sums of Independent Random Variables239
6.4Conditional Distributions: Discrete Case 248
6.5Conditional Distributions: Continuous Case 250
6.6Order Statistics256
6.7Joint Probability Distribution of Functions of Random Variables260
6.8Exchangeable Random Variables267
7 Properties of Expectation280
7.1Introduction 280
7.2Expectation of Sums of Random Variables281
7.3Momentsof the Number of Eventsthat Occur298
7.4Covariance,Variance of Sums,and Correlations304
7.5Conditional Expectation 313
7.6Conditional Expectation and Prediction330
7.7Moment Generating Functions334
7.8Additional Properties of Normal Random Variables345
7.9General Definition of Expecta