I'm trying to compute the exact covariance matrix of normal order statistics.
Well known formulas (listed in Zakkula Govindarajulu, 1962) allow us to compute moments of order statistics, as well as their products, i.e., $E[X_iX_j], E[X_i]E[X_j]$
Does the explicit form of the covariance matrix of normal order statistics exist ? I mean, how to compute the covariance matrix from here ?
~~UPDATE~~ I did not see this : Order statistics of equal correlated continuous random variables
I am on it. -> UPDATE -> I already know this. That's exactly what one can read in Govindarajulu (1962). Excepted for moment products.
UPDATE :Mark L. Stone answered my question.
So, if i want to compute my covariance matrix from "here" : i "just" do $cov(X_i,X_j) = E[X_iX_j] - E[X_i]E[X_j]$