investment tools quantitative methods

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1、三、InvestmentTools:QuantitativeMethods1.A:SamplingandEstimationa:Definesimplerandomsampling.Simplerandomsamplingisamethodofselectingasampleinsuchawaythateachitemorpersoninthepopulationbeginstudiedhasthesame(non-zero)likelihoodofbeingincludedinthesample.Thisisthestandards

2、amplingdesign.b:Defineandinterpretsamplingerror.Samplingerroristhedifferencebetweenasamplestatistic(themean,variance,orstandarddeviationofthesample)anditscorrespondingpopulationparameter(themean,varianceorstandarddeviationofthepopulation). Thesamplingerrorofthemean=samp

3、lemean-populationmean=Xbar-µ.c:DefineasamplingdistributionThesamplestatisticitselfisarandomvariable,soitalsohasaprobabilitydistribution.Thesamplingdistributionofthesamplestatisticisaprobabilitydistributionmadeupofallpossiblesamplestatisticscomputedfromsamplesofthesamesi

4、zerandomlydrawnfromthesamepopulation,alongwiththeirassociatedprobabilities.d:Distinguishbetweensimplerandomandstratifiedrandomsampling.Simplerandomsamplingiswheretheobservationsaredrawnrandomlyfromthepopulation.Inarandomsampleeachobservationmusthavethesamechanceofbeingd

5、rawnfromthepopulation.Thisisthestandardsamplingdesign.?Stratifiedrandomsamplingfirstdividesthepopulationintosubgroups,calledstrata,andthenasampleisrandomlyselectedfromeachstratum.Thesampledrawncanbeeitheraproportionaloranon-proportionalsample.Aproportionalsamplerequires

6、thatthenumberofitemsdrawnfromeachstratumbeinthesameproportionasthatfoundinthepopulation.e:Distinguishbetweentime-seriesandcross-sectionaldata.Atime-seriesisasampleofobservationstakenataspecificandequallyspacedpointsintime.ThemonthlyreturnsonMicrosoftstockfromJanuary1990

7、toJanuary2000areanexampleoftime-seriesdata. Cross-sectionaldataisasampleofobservationstakenatasinglepointintime.ThesampleofreportedearningspershareofallNasdaqcompaniesasofDecember31,2000isanexampleofcross-sectionaldata.f:Statethecentrallimittheoremanddescribeitsimportan

8、ce.Thecentrallimittheoremtellsusthatforapopulationwithameanµandafinitevariance σ2,thesamplingdistributionofthe