Comprehensive code, thorough maths with explanations are needed

Question 2 (40 %) Conduct the following model order selection exercise using 10-fold cross-validation procedure and report your procedure and results in a comprehensive, convincing, and rigorous fashion: 1. Select a Gaussian Mixture Model as the true probability density function for 2-dimensional real-valued data synthesis. This GMM will have 4 components with different mean vectors, different covariance matrices, and different probability for each Gaussian to be selected as the generator for each sample. Specify the true GMM that generates data in a way that has two of the Gaussian components overlap significantly (e.g. set the distance between mean vectors comparable to the sum of their average covariance matrix eigenvalues). 2. Generate multiple data sets with independent identically distributed samples using this true GMM: these datasets will have respectively 10, 100, 1000 samples. 3. For each data set, using maximum likelihood parameter estimation principle (e.g. with the EM algorithm), within the framework of K-fold (e.g.. 10-fold) cross-validation, evaluate GMMs with different model orders: specifically evaluate candidate GMMs with 1,2,...,10 Gaussian components. Note that both model parameter estimation and validation perfor- mance measures to be used is log-likelihood of data. 4. Repeat the experiment multiple times (e.g.. at least 100 times) and report your results, indi- cating the rate at which each of the the six GMM orders get selected for each of the datasets you produced. Develop a good way to describe and summarize your experiment results in the form of tables/figures