1. Generate synthetic from a mixture of three Gaussians. Check the accompanying Jupyter Notebook for this chapter for an example on how to do this. Fit a finite Gaussian mixture model with 2, 3, or 4 components.
2. Use WAIC and LOO to compare the results from exercise 1.
3. Read and run the following examples about mixture models from the PyMC3 documentation ( https://pymc-devs.github.io/pymc3/examples):
   • Marginalized Gaussian Mixture Model (https://docs.pymc.io/notebooks/marginalized_gaussian_mixture_model.html)
   • Dependent density regression (https://docs.pymc.io/notebooks/dependent_density_regression.html)
   • Gaussian Mixture Model with ADVI (https://docs.pymc.io/notebooks/gaussian-mixture-model-advi.html) (you will find more information about ADVI in Chapter 8, Inference Engines)
4. Repeat exercise 1 using a Dirichlet process.
5. Assuming for a moment that you do not know the correct species/labels for the Iris dataset, use a mixture model to cluster the three iris species, using one feature of your choice (like the length of the sepal).
6. Repeat exercise 5 but this time use two features.