Conditional mean of multivariate normal with subset fixed

[lequan]

X (n by 1) follows a multivariate normal distribution, i.e.,

X ~ N(mu, Sigma). mu is n by 1, Sigma is n by n.

What is

E(X|X_{sub}=A)?

where the index 'sub' (m by 1) is a subset of {1,2,..,n}, A is m by 1, 1 <= m < n.

 

[Stephen Tashi]

See if this answers the question: https://onlinecourses.science.psu.edu/stat505/node/43

$E(Y|X=x) = \mu_Y + \Sigma_{YX}\ \Sigma^{-1}_X ( x - \mu_x)$

 

[lequan]

Thanks a lot for the reference! This is the right answer. Actually, this is about the conditional distribution of multivariate normal variables, and well known in any standard textbook of basic statistics. However, I failed to realize this early. :(