Multivariate Analysis : error terms

Hi guys ,

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

X1 = Y1 + Y2 + e1

X2 = Y2 + Y3 + e2

X3 = Y1 + Y1 + e3

where

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

and

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:

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

much thanks