I have no idea for part b and c.

Question 1. [25 MARKS] Imagine that you would like to predict if your favorite table will be free at your favorite restau- rant. The only additional piece of information you can collect, however, is if it is sunny or not sunny. You collect paired samples from visit of the form (is sunny, is table free), where it is either sunny (1) or not sunny (0) and the table is either free (1) or not free(0). (a) [10 MARKS] How can this be formulated as a maximum likelihood problem? Explain what the distributions are, what parameters need to be learned and write the (log) likelihood explicitly for those distributions and parameters. You do not need to solve this maximum likelihood problem. (b) [10 MARKS] Assume you have collected data for the last 10 days and computed the maximum likelihood solution to the problem formulated in (a). You do not actually have to do this, just assume that you did and now have estimated the parameter for your distribution. If it is sunny today, how would you predict if your table will be free? (C) [5 MARKS] Imagine you could further gather information about if it is morning, afternoon, or evening. How does this change the maximum likelihood problem? You do not need to write the log likelihood explicitly for this question, just explain how the distributions and parameters change