Describe the range of a random vector with multivariate normal distribution

Let have covariance matrix .

Note that , so have rank 2. If and has a multivariate normal distribution, describe the range of X.

Solution so far:

Now, since , I have:

So I need to find out when does that happens, but I'm kind of stuck at the moment, any help please? Thanks!

Re: Describe the range of a random vector with multivariate normal distribution

Hey tttcomrader.

What part of R^3 describes this linear equation involving X1, X2, and X3? (Hint: It will be on a plane in 3 dimensional space with two independent parameters).

Re: Describe the range of a random vector with multivariate normal distribution

So since , then we must have for some constant k.

That also means that , which is , so ?

Re: Describe the range of a random vector with multivariate normal distribution