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Imagine that you would like to predict if your favorite table will be free at your favorite restaurant. 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? (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). If it is sunny today, how would you predict if your table will be free? (c) [5 marks] Imagine now that you could further gather information about if it is morning, afternoon, or evening. How does this change the maximum likelihood problem?
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