Chapter 5: Bivariate and Multivariate Probability Distributions: Notes done in LaTeX

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Department
Statistics
Course
STAT265
Professor
Rohana Karunamuni
Semester
Fall

Description
Stats265Chapter5DarrellAucoinTeacherDrRJKarunamuniDecember222011ContentsChapter5BivariateandMultivariateProbabilityDistributions2Introduction2BivariateandMultivariateProbabilityDistributions4PropertiesofUnivariateDistributions5PropertiesofBivariateDistributions5MarginalandConditionalProbabilityDistributions13MarginalProbabilityDistributions13ConditionalProbabilityDistributions14MarginalandConditionalDensityFunctions15IndependentRandomVariables19IndependenceandDependenceProperties26ExpectedValueofaFunctionofRandomVariables26SpecialTheorems29TheCovarianceofTwoRandomVariables332AQuickWaytoFindEXEXEXY33TheExpectedValueandVarianceofLinearFunctionsofRandomVariables43TheMultinomialProbabilityDistribution46MultinomialProbabilities47ConditionalExpectations481Chapter5BivariateandMultivariateProbabilityDistributionsIntroductionDenition1ForadiscreterandomvariableYthefunctionpdenedbypyPYyiscalledtheprobabilitymassfunctionofYExampleHeartsDrawtwocardswithoutreplacementfromadeckofcardsandletHbethenumberofheartsItsprobabilityfunctionisgiveninthefollowingtable01219132P343434Denition2ForanyrandomvariableYthefunctionFdenedbyFyPYyiscalledthedistributionfunctionofYExampleHeartsagainThedistributionfunctionofHisgivenby01219132P34343439C2P052C219P0343913CC11P152C213P1342
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