please solve this

12. Probabilistic Models [15 points] We would like to build a model that predicts a disease D in a patient. Assume we have two classes in our label set t: diseased and healthy. We have a set of binary patient features x = [ri, ..., "x] that describe the various comorbidities of our patient. We want to write down the joint distribution of our model. (a) [4 points] What is the problem in calculating this joint distribution? How many parameters would be required to construct this model? How does the Naive Bayes model handle this problem? (b) [3 points] Write down the joint distribution under the Naive Bayes assumption. How many parameters are specified under the model now? (c) [4 points] Why does the Naive Bayes assumption allow for the model parameters to be learned efficiently? Write down the log-likelihood to explain why. Here, assume that you observed N data points (x), t()) for i = 1, 2. .... N. (d) [1 points] Show how you can use Bayes rule to predict a class given a data point. (e) [3 points] Explain how placing a Beta prior on parameters is helpful for the Naive Bayes model