Problem 1 Two semi-working street lamps turn on and off independently as follows: within each one-minute interval, a lamp that is on turns off with probability p, and a lamp that is off turns on with probability p. At time t = 0, 1, 2... minutes, an observer records the number N, of street lamps that are on, as well as the change De = N, - N-1 from the previous recorded number. (a) Do No, Ni,... form a Markov process? What is the entropy rate of this sequence? (b) Do Do, Di,... form a Markov process? What is the entropy rate of this sequence? Problem 1 Two semi-working street lamps turn on and off independently as follows: within each one-minute interval, a lamp that is on turns off with probability p, and a lamp that is off turns on with probability p. At time t = 0, 1, 2... minutes, an observer records the number N, of street lamps that are on, as well as the change De = N, - N-1 from the previous recorded number. (a) Do No, Ni,... form a Markov process? What is the entropy rate of this sequence? (b) Do Do, Di,... form a Markov process? What is the entropy rate of this sequence