Suppose that the original chain {xn} is recurrent. Is {yn} recurrent? If so, prove it; if not, provide a counterexample.
a) Yes, {yn} is recurrent; prove it.
b) Yes, {yn} is recurrent; provide a counterexample.
c) No, {yn} is not recurrent; prove it.
d) No, {yn} is not recurrent; provide a counterexample.