=+

(c) Verify the following behavior. If s is an even integer and X0 is even, then all subsequent Xn are even. If s is an even integer and X0 is odd, then all subsequent Xn are odd. If s is an odd integer, then the Xn alternate between even and odd values.

What is the period of the chain when s is odd? Recall that the period of state i is the greatest common divisor of the set

{n ≥ 1 : p

(n)

ii > 0}, where p

(n)

ii is an n-step transition probability.

If all states communicate, then every state has the same period.