Why is this multivariate $3\sigma$ ellipse rotated?

Question

While reading this answer, I clicked on the provided link to this Wikipedia page. The main article image shows the PDF of a 2D multivariate normally distributed system:

In the image, the $3\sigma$ ellipse is marked in green. Since the two variable coordinates x and y are normally (and thus symmetrically) distributed around the X and Y axes, I'd expect the ellipse's major and minor axes to be aligned with the X and Y axes. The image shows a slightly rotated ellipse.

Why is the ellipse rotated? Is it just a drawing error?

Answer 1

The random variables $X$ and $Y$ are not independent. As you can tell from the following line in the source code on the image page, there is a correlation between them:

CovMatrix = [1 0.6; 0.6 2];

(The off-diagonal entries in the covariance matrix are non-zero.)