2. Wednesday Saturday Sunday Monday Tuesday Thursday Friday Home Home Home Home 12 am Home Home Home Home Home Home Home Home 1 am Home Home Home Home 2 am Home Home Home Home Home Home Home Home 3 am Home Home Home Home 4 am Home Home Home Home Home Home Home Home Park Home Home Home Home 5 am Home 6 am Home Park Park Grocery Home Home Home Home 7 am Home Park Home Home Park Home 8 am Office Home Office Office Park Home Home Park Office Home Restaurant 9 am Office Office Office Restaurant Park 10 am Office Office Office Office Home Grocery Park 11 am Office Office Office Office Office Park Noon Office Office Office Office Office Grocery Office Home Park 1 pm Office Office Office Office 2 pm Office Office Office Office Office Home Park 3 pm Office Office Office Office Office Home Home Office Office Office Office Home Home 4 pm Office 5 pm Office Office Office Office Office Park Home Office Grocery Park 6 pm Home Restaurant Movie Home Home Home Grocery Restaurant Movie Home Home 7 pm 8 pm Home Home Home Restaurant Movie Restaurant Home Home Home Home Home Home Restaurant 9 pm Home 10 pm Home Home Home Home Home Restaurant Home 11 pm Home Home Home Home Home Home Home Table: User A's Hourly Location Log Consider a smart thermostat (e.g., Nest by Google). The thermostat shuts down the air conditioning system when users are not at home, which should help to save energy. Based on a predictive model, and given the location of the users, the thermostat determines when it should turn on the air conditioning so the temperature is comfortable as soon as the users arrive at their homes (and remains nice until they leave again). Suppose that a particular user (User A) lives alone in a house. User A's hourly location log is provided in the table. This log is available to a mobile application that interfaces with the Nest thermostat. Design a markov chain with 2 states Home and not Home. Consider that the day of the week does not matter. Consider data for all 7 days of the week with equal probability of occurrence when you build the Markov chain. Compute the stationary probability matrix. Assume that it takes 15 minutes for Nest to get the house temperature to 75 degrees, regardless of the starting temperature. Given that it is 9 am and User A is not at home, if the AC restarts at 12:45 pm, what is the probability that User A will arrive home in time with the temperature at 75 degrees? (Write your answer as a decimal and round to the nearest hundredth.) Enter answer here