Transcription of Chapter 2 Multivariate Distributions and Transformations
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Chapter 2 Multivariate Distributions and Transformations
Chapter 2 Multivariate Distributionsand Joint, Marginal and Conditional Distri-butionsOften there arenrandom variablesY1,..,Ynthat are of interest. For exam-ple,age, blood pressure, weight, genderandcholesterol levelmight be someof the random variables of interest for patients suffering from heart <nbe then dimensional Euclidean space. Then thevectory= (y1,..,yn) <nifyiis an arbitrary real number fori= 1,.., ,..,Ynare discrete random variables, then thejointpmf(probability mass function) ofY1,..,Ynisf(y1,..,yn) =P(Y1=y1,..,Yn=yn)( )for any (y1,..,yn) < joint pmffsatisfiesf(y) f(y1,..,yn) 0 y <nand f(y1,..,yn) = :f(y)>0 For any eventA <n,P[(Y1.)]
Chapter 2 Multivariate Distributions and Transformations 2.1 Joint, Marginal and Conditional Distri-butions Often there are nrandom variables Y1,...,Ynthat are of interest.For exam-
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