Hello @Captain_Riggs,
If we put the assignment aside for a moment, then if the underlying distribution is indeed a multivariate Gaussian with a non-diagonal covariance, then we should use that non-diagonal covariance. This point should not be unclear.
As for the assignment, they can control what is the underlying distribution in their question. If I remember correctly, the lectures focus on independent features most if not all of the time, so I will not be surprised if they want to stick with that in the assignment.
Therefore, I very much agree with Paul’s latest reply.
We can argue about the assignment flow, about the inconsistencies. We can also argue that the input data was just a biased subset of a population of which the distribution has diagonal covariance.
But at the end, the assignment wants to show how to compute covariance. It wants to show how to estimate a probability given a certain configuration. In that sense, it serves its purpose.
Cheers,
Raymond