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Multivariate Analysis : error terms

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Hi guys ,


say I have 3 random variables X1,X2 , X3 where


X1 = Y1 + Y2 + e1

X2 = Y2 + Y3 + e2

X3 = Y1 + Y1 + e3



X1,X2,X3 are normally distributed with N(0,1)


e1,e2,e3 are independent random variables (error terms) with normal distribution


Do I have to include the error terms for the mean vector of X and the covariance maxtrix of X , if so how would it look like ?



mean(X) = [mean(X1)mean,(X2),mean(X3)]'


much thanks

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