Let (Xn)nzo and (Yn)n>o be two independent simple symmetric random walks with Xo = x and Yo = y where x, y have the same parity and x > y. (a) Prove that the process (Xn - Yn)n> is a random walk. Determine its state space and transition probabilities. (b) Define T = inf{n 2 1: Xn = Yn}. Prove that P ( T > n) = P( Xn > Yn) - P(Xn