A student takes this course at period 1 on Monday, Wednesday, and Friday. Period 1 starts at 7:25 A.M. Consequently, the student sometimes misses class. The student's attendance behavior is such that she attends class depending only on whether or not she went to the last class. If she attended class on one day, then she will go to class the next time it meets with probability 1/2. If she did not go to one class, then she will go to the next class with probability 3/4.
(a) Find the transition matrix .
(b) Find the probability that if she went to class on Wednesday that she will attend class on Friday.
(c) Find the probability that if she went to class on Monday that she will attend class on Friday.
(d) Does the Markov chain described by this transition matrix have a steady-state distribution? If so, find that distribution