# How do you compute multivariate normal distribution probabilities?

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.

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.)