ESE 502 Tony E. Smith MULTIVARIATE NORMAL DISTRIBUTION 1. Univariate Density. If Xis distributed univariate normal with mean, µ, and variance, 2σ, i.e., if 2(, )XNµσ∼, then the probability density function, 2(; , )xφ, of Xis given by 212212xxeσπφµ−−=21111222()()2(2 )()xxeσµπσ−−−−−−=2. Multivariate Density. If a random vector (:1,.., )iXXin′==is distributed multivariate normal with mean vector, (:1,.., )iinand covariance matrix, (: ,1,.., )ijijnΣ
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