Question: Linear combination of random variables

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[1],epsilon[2]] and then a vector of two correlated gaussian RVs [nu[1],nu[2]]. Both epsilon[1] and epsilon[2] are also uncorrelated with nu[1] and nu[2].

Now I want to create a vector of two correlated gaussian RVs, S, where S[1]=nu[1]+epsilon[1] and S[2]=nu[2]+epsilon[2]. The means and the variances of [S[1],S[2]] are correct, but the covariance (off-diagonal element of the covariance matrix) is weird. How to do this in Maple?

Please check this script:


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