# Bounds for the sum of conditional gaussian random variables Answer

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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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