Chapter 10 Problem Set Name: SECTION 10.4 PROBLEM SET: ABSORBING MARKOV CHAINS 1) Given the following absorbing Markov chain. S 1 S2 S3 S4 S l l 0 0 0 T = $2 .1 .4 .2 .3 S3 0 0 l 0 S4 .4 0 2 4 a) Identify the absorbing states. b) Write the solution matrix. c) Starting from state 4, what is the probability of d) Starting from state 2, what is the probability of eventual absorption in state 1'.' eventual absorption in state 3? Page of414 O 200M + 5) The non-tenured professors at a communin college are regularly evaluated. Aer an evaluation they are classied as good, bad, or improvable. The "improvable" are given a set of recommendations and are re-evaluated the following semester. At the next evaluation, 60% of the improvable turn out to be good, 20% bad, and 20% improvable, These percentages never change and the process continues. a) Write the transition matrix. b) Identify the absorbing states. c) Write the solution matrix. d) What is the probability that a professor who is improvable will eventually become good? 381