MATH 303 Midterm: MATH 303 2013 Winter Test 2
Document Summary
Brief explanation is required whenever it is not clear how answers are obtained. The test has 7 questions and is out of 70. Be sure this exam has 15 pages including the cover. Page 2 of 15: consider the markov chain (xn, n = 0, 1, . whose states and transitions of positive probability are indicated by the oriented arrows in the diagram. One arrow has both orientations; the others only permit transitions in one direction. Solution: {1, 2}, {3, 4, 5, 6, 7}. Page 3 of 15 (e) (3 points) what are the hypotheses in the main theorem about when the long term probability limn pi(xn = j) exists and does not depend on i. Solution: the markov chain (xn, n = 0, 1, . is irreducible, aperiodic and positively recurrent. (f) (1 point) do the hypotheses you stated in part (e) hold for (xn, n = 0, 1, .
