Every day, Eric takes the same street from his home to the university. There are 4 street lights along his way. and Eric has noticed the following Markov dependence. If he sees a green light at an intersection, then 60% of time the next light is also green, and 40% of time the next light is red. However, if he sees a red light, then 70% of time the next light is also red, and 30% of time the next light is green. A. Construct the transition probability matrix for the street lights.
B. If the first light is green, what is the probability that the third light is red?
C. Eric's classmate Jacob has many street lights between his home and the university. If the first street light is green, what is the probability that the last street light is red? (Use the steady-state distribution.)