Fall 2011 Strategic Practice 11: Section 2 (Multivariate Normal) - Question 1
Show that if $(X_{1}, X_{2}, X_{3})$ is Multivariate Normal, then so is the subvector $(X_{1}, X_{2})$.
Solution: Consult iTunes course for full detailed solutions. Any linear combination t1X1 + t2X2 can be thought of as a linear combination of X1, X2, X3 (where the coefficient of X3 is 0), so t1X1 + t2X2 is Normal for all t1, t2, which shows that (X1, X2) is MVN.
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."