In my machine learning notes for Gaussian Mixture Models, I see the following statement:
It is common to confuse a mixture of Gaussian with a sum of Gaussians. Note that, a sum of Gaussian RVs is another Gaussian, and therefore unimodel.
This is only true if the sum of Gaussian RVs is a sum of independent Gaussian RVs right? If there is any dependency, does this guarantee that the sum of gaussians is NOT gaussian?