 Let x1*...,xs* be another finite collection of variables, it's obvious that 

formula_47, 

where formula_48, formula_49, formula_50.According to the equations above, the outputs y are also jointly distributed according to a multivariate Gaussian.Thus, 

formula_51, 

where formula_52, formula_53, formula_54, and formula_55 is formula_56 identity matrix.