Week 1.2: Random vectors, multivariate normal distributions

Question 1

What is the marginal density of a variable which is multivariate normal? Parameters?

Answer 1

It is also normal with parameters mu_i and sigma^2_i.

Question 2

May different marginal pdf’s have the same joint pdf, or may different joint pdf’s have the same marginal pdf’s?

Answer 2

Different joint pdf’s may have the same marginal pdf’s.