Statistical Theory

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1、COURSENOTESSTATS210StatisticalTheoryDepartmentofStatisticsUniversityofAucklandContents1.Probability31.1Introduction......................................31.2Samplespaces.....................................31.3Events.........................................5

2、1.4Partitioningsetsandevents.............................121.5Probability:awayofmeasuringsets........................141.6Probabilitiesofcombinedevents...........................171.7ThePartitionTheorem................................191.8Examplesofbasicprob

3、abilitycalculations.....................201.9Formalprobabilityproofs:non-examinable.....................221.10ConditionalProbability................................241.11Examplesofconditionalprobabilityandpartitions.................291.12Bayes’Theorem:invert

4、ingconditionalprobabilities................311.13Chainsofeventsandprobabilitytrees........................341.14Simpson’sparadox..................................381.15Probabilitiesfromcombinatorics:equallylikelyoutcomes.............391.16StatisticalIndepend

5、ence...............................421.17RandomVariables...................................451.18KeyProbabilityResultsforChapter1.......................492.DiscreteProbabilityDistributions512.1Introduction......................................512.2Theprobabi

6、lityfunction,fX(x)...........................522.3Bernoullitrials....................................542.4Exampleoftheprobabilityfunction:theBinomialDistribution.........552.5Thecumulativedistributionfunction,FX(x)....................592.6Hypothesistesting..

7、................................632.7Example:Presidentsanddeep-seadivers......................702.8Example:Politiciansandthealphabet.......................772.9Likelihoodandestimation..............................802.10Randomnumbersandhistograms.............

8、.............922.11Expectation......................................952.12Variabletransformations...............................1012.13Variance........................................1072.14Mean