@Framework，，，｀｀｀｀｀｀｀、＼、、、、、、、、、、、、、、、、、、、、I、I、~、－－－---圈--夕夕夕，，，，，，，，，，，，，，，，，，，，，I，III，，，-2-1231.Probability2.BasicStatistics3.Distributions4.HypothesisTestsandConfidenceIntervals5.LinearRegression6.ElementsOfForecasting(New)7.SimulationModeling8.EstimatingVolatilitiesandCorrelations芸业．创新.1首值一Covariance►CovarianceCov(X,Y)=E[(X-E(X))(Y-E(Y))]=E(XY)-E(X)E(Y)1nSxv=区(Xi戊）(Yi-Y)n-1仁1•Covariancemeasureshowonerandomvariablemoveswithanotherrandomvariable.•Covariancerangesfromnegativeinfinitytopositiveinfinity.16-123芸业．创新.1首值一BinomialDistribution•BernoulliDistribution•P(X=1)=pP(X=0)=1-p►BinomialDistribution•Theprobabilityofxsuccessesinntrailsn!p(x)==P(X==x)==C歹(l-p)n-x==px(l-p)n-xx!(n-x)!IExpectationVarianceIBernoullirandomvariablepp(l-p)Binomialrandomvariablenpnp(l-p)26-123芸业．创新.1首值一TheStandardNormalDistribution►Thestandardnormaldistribution•N(0,1)orZ•Standardization:ifX-N(µ,矿），thenX-µZ==1'JN(0,1)a•Z-table►Howweusethestandardnormaldistributiontocomputevarious•Example:X,...,N(70,9),computetheprobabilityofX�64.12.✓Z=X-µ64.12-70�-1.9603✓P(Z�-1.96)=0.0250•Question1:computetheprobabilityofX�75.9.•Question2:computetheprobabilityof64.12�X�75.9.31-123芸业．创新.1首值一ContinuousProbabilitvDistribution►Student'stdistribution•Itissimilartothenormal,exceptitexhibitsslightlyheaviertails.t=X-µx-tsxIJnn-1✓Itissymmetrical.✓Ithasmeanofzero.•Asthed.f.increasethet-distributionconvereswiththestandardnormaldistribution.•Boththenormalandstudent'stdistributioncharacterizethesamplingdistributionofthesamplemean.Thedifferenceisthat血normalisusedwhenweknowtheoulationvariance.功旦student'stisusedwhenwemustrelonthesamlevariance.Inpractice,wedon'tknowthepopulationvariance,sothestudent'stdistributionistypicallyappropriate.32-123芸业．创新.1首值一www.gfedu.netContinuousProbabilityDistribution►LognormalDistribution•IflnXisnormalthenXislonormal·ifavariableislonormalits...
