# 09_28 - STAT 410 Examples for 1 2 E X = = n Fall 2011 X1 X2...

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STAT 410 Examples for 09/28/2011 Fall 2011 X = n X ... X X 2 1 n -dimensional random vector E ( X ) = μ = n ... 2 1 μ Σ = nn n n n n σ ... ... ... ... ... ... 2 1 2 22 21 1 12 11 ij = Cov ( X i , X j ) Σ = E [ ( X μ ) ( X μ ) ' ] Σ – symmetric, positive-definite Multivariate Normal Distribution: X ~ N n ( μ , Σ ) f X ( x ) = ( ) ( ) ( ) - - - - μ x μ x Σ Σ 1 2 1 2 2 1 exp 2 1 ' n π Z ~ N n ( 0 , I n ) f Z ( z ) = ( ) - z z 2 2 1 exp 2 1 ' n = = - n i i z 1 2 2 1 exp 2 1 X = Σ 1/2 Z + μ M X ( t ) = + t t μ t Σ 2 1 exp ' ' t = n t t t ... 2

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## This note was uploaded on 10/31/2011 for the course MATH 464 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.

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09_28 - STAT 410 Examples for 1 2 E X = = n Fall 2011 X1 X2...

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