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Bounds for the sum of conditional gaussian random variables

Let $X_1,…,X_n$ breathe $n$ gaussian random variables $N(0,1)$ not essentially unbiased or collectively correlated, $S=sum_{i=1}^n w_i X_i$ breathe the weighted sum of those gaussian variables (as a result of $(X_i)_{i=1,..,n}$ usually are not collectively correlated, $S$ can breathe non usually distributed)

1/ What are the higher certain and/or scowl certain of $P(S leq x)$ $forall xin mathbb{R}$?

2/ And what are the higher certain and/or scowl certain of $P(S leq x)$ if we all know the covariance matrix $Omega$ of those $n$ gaussian random variables?

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