MultivariateNormalDistr.pdf - Multivariate Normal Distribution Y Nn if f(y1 yn = n 2(2 | 1 2 1 1 exp(y)0 1(y 2 where < yi <(i = 1 2 n and is an n n

MultivariateNormalDistr.pdf - Multivariate Normal...

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Multivariate Normal Distribution: Y N n ( θ , Σ ) if f ( y 1 , . . . , y n ) = (2 π ) n 2 | Σ | 1 2 - 1 exp " - 1 2 ( y - θ ) 0 Σ - 1 ( y - θ ) # where -∞ < y i < ( i = 1 , 2 , . . . , n ) and Σ is an n × n positive definite matrix. Theorem: If Y N n ( θ , Σ ) then ( Y - θ ) 0 Σ - 1 ( Y - θ ) χ 2 n . Corollary: If Y N n ( θ , Σ ) then Y - θ N n ( 0 , Σ ). Theorem: If Y N n ( θ , Σ ) and C is a p × n matrix of rank p , then CY N p ( , C Σ

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