I am working on this problem and I am stuck because of my lack of understanding of marginal and conditional distributions.
We have two random vectors x and z which both have gaussian distributions defined as: N(Ux, Cx) and N(Uz,Cz) (where Ux and Uz are the means and Cx and Cx are covariance matrices). We define a third vector y such that y = x + z. The problem is to find the marginal distribution of y.
I believe I can assume the vector y has a gaussian distribution with the following characteristics, N(Ux + Uz, Cx + Cz). Essentially I am saying the sum of two random vectors having gaussian distributions will create a new random vector following a gaussian distribution where the mean and covariance is the sum of the means and covariances of the individual vectors.
Even if my distribution for y is correct, I dont understand what is meant by the "marginal distribution of y" which is what I am supposed to find an expression for.
Any hints or help with understanding these concepts.