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3 Random vectors and multivariate normal distribution

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CHAPTER3ST 732,M. DAVIDIAN3Randomvectorsandmultivariatenor maldistributionAswe saw in Chapter1, a naturalway to thinkaboutrepeatedmeasurement datais as a seriesofrandomvectors, onevectorcorrespondingto each in which thesevectorsofmeasurements turnoutis governedby probability, we needtodiscussextensionsof usualunivari-ateprobability distributionsfor(scalar)randomvariablest omultivariateprobability ,it is wiseto reviewtheimportant conceptsof randomvariableandprobability distributionandhow we usetheseto :We may thinkof arandomvariableYas a characteristicwhosevaluesmayvary. Theway it takes onvaluesis described by aprobability ,REPEATED:It is customaryto useupper caseletters, , to denotea genericrandomvariableandlower caseletters, , to denotea particularvaluethattherandomvariablemay take onor thatmay be observed(data).

3 Random vectors and multivariate normal distribution As we saw in Chapter 1, a natural way to think about repeated measurement data is as a series of random vectors, one vector corresponding to …

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