Code up the the EM algorithm for mixtures of univariate normals.
There are lots of things to try!!
If you want you can spend all your time on the univariate mixtures!!
But if you get that working ok, pretty fast, you should be keen to do:
Code up the the EM algorithm for mixtures of multivariate normals.
There are lots of things to try!!
I would start with \(p=2\) !!