And very surprisingly, the resulting Gaussian is more certain than the two-component Gaussians. That is the covariance is smaller than either of the two covariances in the installation. Intuitively speaking, this is the case because we actually gain information. The two Gaussians together with high information content in either Gaussian installation. So it look like something like this. And it is completely non-obvious. You might have to take this with faith, but I can actually prove it to you.