Summary: ISyE 6761 Exam # 2
Please be neat and show all your work so that I can give you partial credit.
1. a. (10) Show that the period of a state in an irreducible Markov chain with
N states is less than or equal to N.
b. (10) Show that there are no null recurrent states in a Markov chain with
finite state space.
c. (10) Show that not all states in a Markov chain with finite state space are
2. (25) Let Xn be the sum of the first n outcomes of tossing of a six sided fair
die repeatedly in an independent fashion. Compute