# Reconstruction from statistics

imagine to have data like the following

$$\begin{matrix}X1 & X2 & X3 \\\ 1 & 2 & 3\\\ 4 & 5 & 6\\\ 7 & 8 & 9\\\ \dots\end{matrix}$$

where each row is a multivariate Gaussian (0, $$\Sigma$$).

Having the first order statistics for each column (mean, variance, median, min, max) + the covariance matrix, is it possible to get the third column knowing the other ones?

• Do you mean to ask if you can solve exactly for the third column? (unless the number of rows is very small) that is not possible. – kjetil b halvorsen Jan 30 at 3:26