Question

Consider a simplification of the autonomous vehicle project we discussed in the lecture on Markov processes. The process has three states that describe the driving environment: s1 := “driving in city,” s2 := “driving in suburbs,” s3 := “driving in rural area (‘country’).” If the car is driving in the city, there is a 50% chance the next passenger pickup assignment will also be in the city. If the car is driving in the suburbs, there is a 40% chance the next passenger pickup assignment will be in the suburbs. If the car is driving in the country, there is a 20% chance the next passenger pickup assignment will also be in the country. Anytime there is a switch from the driving environment, it is equally likely to be to either of the other two environments.

a. (1 pt) What is the transition matrix for this process, P?

b. (1 pt) If the car starts in the city, what is the probability that the tenth passenger pickup will be in the country?

c. (1 pt) Suppose a typical drive in the city results in asset depreciation (loss from wear-and-tear) of $10; for the suburbs depreciation is $5, and for the country it is $3. What is the expected loss from depreciation after the 100’th passenger?

Answer 1