1. Every day, Eric takes the same street from his home to theuniversity. There are 4 street lights along his way, and Eric hasnoticed the following Markov dependence. If he sees a green lightat 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 redlight, then 75% of time the next light is also red, and 25% of timethe next light is green. Let 1 = “green light” and 2 = “red light”with the state space {1, 2}.
(a) Construct the 1-step transition probability matrix for thestreet lights.
(b) If the first light is red, what is the probability that thethird light is red?
(c) Eric’s classmate Jacob has many street lights between hishome and the university. If the first street light is red,what is the probability that the last street light is red?(Use the steady-state distribution.)
