What do we need to implement the EM (Expectation Maximization) algorithm ?

The following components are required:

0. Matrix calculations foundation

0.1. Product
0.2. Transposition
0.3. Escalar product
0.4. Determinant
0.5. Sum

Hopefully no matrix inversion would be needed!!!!

1. Multivariate normal probability function (Multinomial) 

2. Mean and standard deviation estimation function (Maximum likelihood)

3. Covariance calculation function (which is the standard deviation source)

4. Some nice plotting can help to show the result

5. Looks like the most complex component would be the Acumulated Multivariate, it involves multiple integrals, basically a numeric method need to be used, to do that we need to research on:

5.1. Montecarlo integration methods

5.2. Cholesky matrix decomposition