How do you compute multivariate normal distribution probabilities?

Question

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.

score 1 · Answer 1 · edited Apr 13 '17 at 12:21

1

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.)

edited Apr 13 '17 at 12:21

Community

1

answered Apr 21 '16 at 23:08

grand_chat

40,909

ah! of course, thanks! – Benjamin Whitesell Apr 22 '16 at 00:55

How do you compute multivariate normal distribution probabilities?

1 Answers1