第1章　概率1
1.1　概率的性質(zhì)1
1.2　計(jì)數(shù)方法11
1.3　條件概率20
1.4　獨(dú)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(jī)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(xiàng)分布63
2.5　超幾何分布71
2.6　負(fù)二項(xiàng)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(jī)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(jī)變量函數(shù)的分布169
5.1　一個(gè)隨機(jī)變量的函數(shù)169
5.2　兩個(gè)隨機(jī)變量的變換178
5.3　多個(gè)獨(dú)立隨機(jī)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(jī)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(diǎn)估計(jì)233
6.1　描述性統(tǒng)計(jì)233
6.2　探索性數(shù)據(jù)分析245
6.3　 順序統(tǒng)計(jì)量256
6.4　最大似然估計(jì)法和矩估計(jì)法264
6.5　簡(jiǎn)單回歸問(wèn)題277
6.6　最大似然估計(jì)量的漸近分布285
6.7　充分統(tǒng)計(jì)量290
6.8　貝葉斯估計(jì)298
第7章　區(qū)間估計(jì)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(jì)假設(shè)檢驗(yàn)361
8.1　單均值檢驗(yàn)361
8.2　兩均值相等的檢驗(yàn)369
8.3　方差檢驗(yàn)378
8.4　比例的檢驗(yàn)385
8.5　分布自由的一些檢驗(yàn)392
8.6　統(tǒng)計(jì)檢驗(yàn)的功效函數(shù)403
8.7　最佳臨界區(qū)域410
8.8　似然比檢驗(yàn)418
第9章　其他檢驗(yàn)425
9.1　卡方擬合優(yōu)度檢驗(yàn)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(jì)和2k析因設(shè)計(jì)465
9.6　回歸和相關(guān)性檢驗(yàn)471
9.7　統(tǒng)計(jì)質(zhì)量控制477
附錄A　參考文獻(xiàn)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