MULTIVARIATE_NORMAL

MULTIVARIATE_NORMAL - ESE 502 Tony E. Smith MULTIVARIATE...

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ESE 502 Tony E. Smith MULTIVARIATE NORMAL DISTRIBUTION 1. Univariate Density . If X is distributed univariate normal with mean, µ , and variance, 2 σ , i.e., if 2 (, ) XN µσ , then the probability density function , 2 (; , ) x φ , of X is given by 2 1 2 2 1 2 x xe σπ φµ    = 21 11 1 22 2 () ( ) 2 (2 ) ( ) xx e σµ πσ −−− = 2. Multivariate Density . If a random vector ( : 1,. ., ) i X Xi n == is distributed multivariate normal with mean vector, ( : 1,. ., ) i in and covariance matrix, ( : , 1,. ., ) ij ij n Σ
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