Problem 3: (40 points): You are an interplanetary search and rescue expert who has just received an urgent message: a rover on Mercury has fallen and become trapped in Death Ravine, a deep, narrow gorge on the borders of enemy territory. You zoom over to Mercury to investigate the situation. Death Ravine is a narrow gorge 6 miles long, as shown below. There are volcanic vents at locations A and D, indicated by the triangular symbols at those locations. The rover was heavily damaged in the fall, and as a result, most of its sensors are broken. The only ones still func- tioning are its thermometers, which register only two levels: hot and cold. The rover sends back evidence E-hot when it is at a volcanic vent (A and D), and E = cold otherwise. There is no chance of a mistaken reading. The rover fell into the gorge at position A on day 1, so X1-A. Let the rover's position on day t be . E {A, B, C, D, E, F). The rover is still executing its original programming, trying to move 1 mile east (i.e. right, towards F) every day. However, because of the damage, it only moves east with probability 0.5, and it stays in place with probability 0.5. Your job is to figure out where the rover is, so that you can dispatch your rescue-bot Problem 3: (40 points): You are an interplanetary search and rescue expert who has just received an urgent message: a rover on Mercury has fallen and become trapped in Death Ravine, a deep, narrow gorge on the borders of enemy territory. You zoom over to Mercury to investigate the situation. Death Ravine is a narrow gorge 6 miles long, as shown below. There are volcanic vents at locations A and D, indicated by the triangular symbols at those locations. The rover was heavily damaged in the fall, and as a result, most of its sensors are broken. The only ones still func- tioning are its thermometers, which register only two levels: hot and cold. The rover sends back evidence E-hot when it is at a volcanic vent (A and D), and E = cold otherwise. There is no chance of a mistaken reading. The rover fell into the gorge at position A on day 1, so X1-A. Let the rover's position on day t be . E {A, B, C, D, E, F). The rover is still executing its original programming, trying to move 1 mile east (i.e. right, towards F) every day. However, because of the damage, it only moves east with probability 0.5, and it stays in place with probability 0.5. Your job is to figure out where the rover is, so that you can dispatch your rescue-bot