Transition matrix

2. A Markov chain with state space {1, 2, 3} has transition probability matrix 00 0.3 0.1 a: 0.3 0.3 0.4 0.4 0.1 0.5 (a) Is this Markov chain irreducible? Is the Markov chain recurrent or transient? Explain your answers. (b) What is the period of state 1? Hence deduce the period of the remaining states. Does this Markov chain have a limiting distribution? (c) Consider a general three-state Markov chain with transition matrix 3011 3012 1013 P = P21 P22 P23 1031 P32 P33 Give an example of a specic set of probabilities jag-'3; for which the Markov chain is not irreducible (there is no single right answer to this1 of course l]. Figure 1.2 4.0 Grades in Economics (G.P.A) 4.0 Grades in English (G.P.A) The PPC in Figure 1.2 indicates a student who: a. is equally proficient in Economics and English. O b. is more proficient at Economics than English O c. prefers Economics over English. d. is more proficient at English than Economics. e. prefers English over Economics.Economics that involves opinion about what ought to he or what should happen, rather than theories that could be tested, would he called... Select one: 0 scarcity macroeconomics subjective values microeconomics rationing free goods rational decisionmaking scarce goods economics normative economics positive economics OOOOOOOOOOO ceteris parihus The fact that the F'F'F usually bows away from the origin implies that ii? getting more of one good means getting more of another good. as the production of any good increases. there is an increase in the opportunity cost of producing it. getting more of one good means getting less of another good- as the production of any good increases. there is a decrease in the opportunity cost of producing it. Problem 7.4 (10 points) A Markov chain X0,X1, X2, . . . with state space S = {1, 2, 3, 4} has the following transition graph: (a) Provide the transitiOn matrix fer the Markov chain. (13) Determine all recurrent and all transient states