MATH 632 Final: 2003 Math 632 - Fall Final Exam
Document Summary
Points add up to 200: consider the discrete-time markov chain with state space. Does there exist an invariant distribution for this chain that is not reversible? (b) (20 pts) let t2 = min{n 1 : xn = 2} be the time of the rst visit to state 2 after time 0. Find e0[t2], the expected time to reach state 2 starting from state 0. (c) (20 pts) let t 2. 1 be the time of the second visit to state 1 after time: find e0[t 2 (in parts (b) and (c), give answers for all values of the parameters, not just the ones for which exists. 1 ]: (50 pts) suppose you have two printers, one connected to your com- If the working printer breaks down, puter and the other one for a spare. it is immediately taken to the shop for repair, and the spare printer is con- nected to the computer.
