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Given a vector $$ X = (X1,X2,X3)^t $$ which is multivariate normal with mean 0 and covariance matrix $$ \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 3 \end{array} \right) $$

find $$ P(X1 > X2 + X3 +2) $$

I dont think anything involving the pdf is the easiest way.

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Hint: $X_1-X_2-X_3$ is normally distributed. What are its mean and variance? (See this post for the variance of a sum of correlated RVs.)

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  • $\begingroup$ ah! of course, thanks! $\endgroup$ Apr 22, 2016 at 0:55

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