1. Formulation of unconditional density estimation of mixture of Gaussians as ML estimation of parameters of a marginal density.

2. Introduction of complete log-likelihood and expected complete log-likelihood, and their connection with E and M steps of EM algorithm

3. Solution of M-step to obtain update equation for means, and interpretation of this as involving soft assignment to Gaussians.

4. Rederivation and explanation of the proof that the EM algorithm leads to monotonic increase of marginal log-likelihood.