I have learned that the conditional distribution of X1, given that X2 = x2 is normal and has covariance = ∑11 - ∑12 (∑22 )^-1∑21
However, I realized that I was using the fact without knowing why?
How does covariance become like that? I was trying to figure it out from book and internet sources but I couldn't figure it out.
Can anyone help me?