How would you simulate a vector or random variables that has a known
mean vector and a known variance-covariance matrix?

Hi

easy way is this:

1) Take n independent normal variables with variance 1 and mean 0

n is dimension of your linear space
arrange them inro a vector v

2) make a linerar transformation    X.i =  L.i/j * v.j

3) L is a matrix which you get by diagonalising your given variance (or rather
it's inverse)

4) X.i = X.i + B.i   will chage means as needed.



re 3)
http://ltcconline.net/greenl/courses/203/MatrixOnVectors/diagonalization.htm
http://en.wikipedia.org/wiki/Diagonalizable_matrix


re 1) 
http://en.wikipedia.org/wiki/Multivariate_normal_distribution

http://www-math.mit.edu/~panchenk/class443/lectures/lecture4.pdf
https://netfiles.uiuc.edu/jimarden/www/Classes/STAT571/chapter3.pdf
 
Hope this will work for you

Hedgie

Complete and concise answers.  Perfect.