Linear combinations of random variables: why Maple does not "inherit" the distributional assumptions when adding up two random variables?
In the script I attach below, I first define a vector of two uncorrelated gaussian RVs [epsilon,epsilon] and then a vector of two correlated gaussian RVs [nu,nu]. Both epsilon and epsilon are also uncorrelated with nu and nu.
Now I want to create a vector of two correlated gaussian RVs, S, where S=nu+epsilon and S=nu+epsilon. The means and the variances of [S,S] are correct, but the covariance (off-diagonal element of the covariance matrix) is weird. How to do this in Maple?
Please check this script: