第1章　概率1
1.1　概率的性質(zhì)1
1.2　計數(shù)方法11
1.3　條件概率20
1.4　獨立事件29
1.5　貝葉斯定理35
第2章　離散分布41
2.1　離散型隨機變量41
2.2　數(shù)學(xué)期望47
2.3　特殊的數(shù)學(xué)期望53
2.4　二項分布63
2.5　超幾何分布71
2.6　負(fù)二項分布76
2.7　泊松分布81
第3章　連續(xù)分布91
3.1　連續(xù)型隨機變量91
3.2　指數(shù)、伽馬和卡方分布100
3.3　正態(tài)分布110
3.4　其他模型119
第4章　二元分布129
4.1　離散型二元分布129
4.2　相關(guān)系數(shù)139
4.3　條件分布145
4.4　連續(xù)型二元分布153
4.5　二元正態(tài)分布162
第5章　隨機變量函數(shù)的分布169
5.1　一個隨機變量的函數(shù)169
5.2　兩個隨機變量的變換178
5.3　多個獨立隨機變量187
5.4　矩母函數(shù)技術(shù)194
5.5　與正態(tài)分布相關(guān)的隨機函數(shù)199
5.6　中心極限定理207
5.7　離散分布的近似213
5.8　切比雪夫不等式和依概率收斂220
5.9　矩母函數(shù)的極限224
第6章　點估計233
6.1　描述性統(tǒng)計233
6.2　探索性數(shù)據(jù)分析245
6.3　 順序統(tǒng)計量256
6.4　最大似然估計法和矩估計法264
6.5　簡單回歸問題277
6.6　最大似然估計量的漸近分布285
6.7　充分統(tǒng)計量290
6.8　貝葉斯估計298
第7章　區(qū)間估計307
7.1　均值的置信區(qū)間307
7.2　兩均值差的置信區(qū)間314
7.3　比例的置信區(qū)間323
7.4　樣本容量329
7.5　百分位數(shù)的分布自由置信區(qū)間337
7.6　更多回歸344
7.7　重抽樣方法353
第8章　統(tǒng)計假設(shè)檢驗361
8.1　單均值檢驗361
8.2　兩均值相等的檢驗369
8.3　方差檢驗378
8.4　比例的檢驗385
8.5　分布自由的一些檢驗392
8.6　統(tǒng)計檢驗的功效函數(shù)403
8.7　最佳臨界區(qū)域410
8.8　似然比檢驗418
第9章　其他檢驗425
9.1　卡方擬合優(yōu)度檢驗425
9.2　列聯(lián)表435
9.3　單因素方差分析446
9.4　雙因素方差分析456
9.5　廣義析因設(shè)計和2k析因設(shè)計465
9.6　回歸和相關(guān)性檢驗471
9.7　統(tǒng)計質(zhì)量控制477
附錄A　參考文獻489
附錄B　表491
附錄C　奇數(shù)習(xí)題答案513
附錄D　數(shù)學(xué)技術(shù)綜述525
索引545



CONTENTS
1 PROBABILITY1
1.1 PropertiesofProbability1
1.2 MethodsofEnumeration11
1.3 ConditionalProbability20
1.4 IndependentEvents29
1.5 Bayes’Theorem35
2 DISCRETEDISTRIBUTIONS41
2.1 RandomVariablesoftheDiscreteType41
2.2 MathematicalExpectation47
2.3 SpecialMathematicalExpectations53
2.4 TheBinomialDistribution63
2.5 TheHypergeometricDistribution71
2.6 TheNegativeBinomialDistribution76
2.7 ThePoissonDistribution81
3 CONTINUOUSDISTRIBUTIONS91
3.1 RandomVariablesoftheContinuousType91
3.2 TheExponential,Gamma,andChi-SquareDistributions100
3.3 TheNormalDistribution110
3.4 AdditionalModels119
4 BIVARIATEDISTRIBUTIONS129
4.1 BivariateDistributionsoftheDiscreteType129
4.2 TheCorrelationCoefficient139
4.3 ConditionalDistributions145
4.4 BivariateDistributionsoftheContinuousType153
4.5 TheBivariateNormalDistribution162
5 DISTRIBUTIONSOFFUNCTIONSOFRANDOMVARIABLES169
5.1 FunctionsofOneRandomVariable169
5.2 TransformationsofTwoRandomVariables178
5.3 SeveralIndependentRandomVariables187
5.4 TheMoment-GeneratingFunctionTechnique194
5.5 RandomFunctionsAssociatedwithNormalDistributions199
5.6 TheCentralLimitTheorem207
5.7 ApproximationsforDiscreteDistributions213
5.8 Chebyshev’sInequalityandConvergenceinProbability220
5.9 LimitingMoment-GeneratingFunctions224
6 POINTESTIMATION233
6.1 DescriptiveStatistics233
6.2 ExploratoryDataAnalysis245
6.3 OrderStatistics256
6.4 MaximumLikelihoodandMethodofMomentsEstimation264
6.5 ASimpleRegressionProblem277
6.6 AsymptoticDistributionsofMaximumLikelihoodEstimators285
6.7 SufficientStatistics290
6.8 BayesianEstimation298
7 INTERVALESTIMATION307
7.1 ConfidenceIntervalsforMeans307
7.2 ConfidenceIntervalsfortheDifferenceofTwoMeans314
7.3 ConfidenceIntervalsforProportions323
7.4 SampleSize329
7.5 Distribution-FreeConfidenceIntervalsforPercentiles337
7.6 MoreRegression344
7.7 ResamplingMethods353
8 TESTSOFSTATISTICALHYPOTHESES361
8.1 TestsAboutOneMean361
8.2 TestsoftheEqualityofTwoMeans369
8.3 TestsforVariances378
8.4 TestsAboutProportions385
8.5 SomeDistribution-FreeTests392
8.6 PowerofaStatisticalTest403
8.7 BestCriticalRegions410
8.8 LikelihoodRatioTests418
9 MORETESTS425
9.1 Chi-SquareGoodness-of-FitTests425
9.2 ContingencyTables435
9.3 One-FactorAnalysisofVariance446
9.4 Two-WayAnalysisofVariance456
9.5 GeneralFactorialand2kFactorialDesigns465
9.6 TestsConcerningRegressionandCorrelation471
9.7 StatisticalQualityControl477
APPENDICES
A REFERENCES489
B TABLES491
C ANSWERSTOODD-NUMBEREDEXERCISES513
D REVIEWOFSELECTEDMATHEMATICALTECHNIQUES525
D.1AlgebraofSets525
D.2MathematicalToolsfortheHypergeometricDistribution529
D.3Limits532
D.4InfiniteSeries533
D.5Integration537
D.6MultivariateCalculus539
Index545