Question

Problem . (25 points) A lost tourist arrives at a point with 3 roads. The first road brings him back to the same point after 1 hour of walk. The second road brings him back to the same point after 6 hours of travel. The last road leads to the city after 2 hours of walk. There are no signs on the roads. Assuming that the tourist chooses a road equally likely at all times, what is the mean time until the tourist arrives to the city?

Answer 1

Answer Date: -17/5/2019 This exercise uses conditional expectation. Let T the time it takes to reach the city, and Di the event the tourist chooses door i for i = 1, 2, 3. To com pute E[T] we will condition on the door scalper picks at the first time: where in 2.1 we use the fact that after each return to the point, the tourist does not keep memory of its past chooses. Rearranging the terms in the last equation, we obtain E[T] = 9