11. Jessica is interested in identifying states in U.S.A. Specifically, she categorizes states into one of three categories based on their longitudes: State = [West, Middle, East]. Jessica further notices three features for each state: (1) Population = [overpopulated, underpopulated] (2) Weather = [cold, warm] (3) Polity = [democratic, republic]. For the sub questions below, we suppose that those 3 features (Population, Weather and Polity) are all conditionally independent given State. Additionally, the following probability values are known to us: (4) Please express P(State/Population, Weather, Polity) by applying Bayes rule. You may need to involve, (one or several) terms where each term is the summation over all possible values for some variables. (4pts) (5) After Jessica selects a state, she identifies the following features: Population=overpopulated, Weather=cold, Polity=republic. What is the probability that the state is one of west states? (4pts)