Consider a Markov chain in steady state. Say that a k length run of zeroes ends at time m if Xm−k−1 = 0, Xm−k = Xm−k+1 = ... = Xm−1 = 0, Xm = 0 Show that the probability of this event is π0(P0,0)k−1(1− P0,0)2, where π0 is the limiting probability of state 0.