1. For the example in the Covariance functions and kernels section make sure you understand the relationship between the input data and the generated covariance matrix. Try using other input such as data = np.random.normal(size=4)
2. Rerun the code generating Figure 7.3 and increase the number of samples obtained from the GP-prior to around 200. In the original figure the number of samples is 2. Which is the range of the generated values?
3. For the generated plot in the previous exercise. Compute the standard deviation for the values of  at each point. Do this in the following form:

• • Visually, just observing the plots
  • Directly from the values generated from stats.multivariate_normal.rvs
  • By inspecting the covariance matrix (if you have doubts go back to exercise 1)

    Did the values you get from these 3 methods agree?

4. Re-run the model model_reg and get new plots but using as test_points X_new np.linspace(np.floor(x.min()), 20, 100)[:,None]. What did you observed? How is this related to the specification of the GP-prior?
5. Go back to exercise 1, but this time use a linear kernel (see the accompanying code for a linear kernel)
6. Go and check the section https://docs.pymc.io/notebooks/GP-MeansAndCovs.html from PyMC3' documentation
7. Run a logistic regression model for the space_flu data. What do you see? Can you explain the result?
8. Change the logistic regression model in order to fit the data. Tip, use an order two polynomial.
9. Compare the model for the coal mining disaster with the one from the PyMC3 documentation (https://docs.pymc.io/notebooks/getting_started.html#Case-study-2:-Coal-mining-disasters). Describe the differences between both models in terms of model-specification and results.