Recall the ones runs Markov chain (Yn) with state space Nand transition probabilities p(i, i + 1) = p(i, 0) = 1/2 for every i ∈N.

a) compute p4(0, 3).

b) prove or otherwise explain the following statement: for each i and n, pn(i, 0) = 1/2.

c) show that state 0 is recurrent.