Stochastic Processes-Random walk around the clock: Consider a Markov chain on S = {1,2,...,12} such that pij = 1/2 if i,j are adjacent hours on a clock, and pij = 0 otherwise.
Suppose that instead, for some p ?≠? 1/2, we have that pij = p (resp. pij = 1 ≠ p) if j is clockwise (resp. counter-clockwise) adjacent to i, and pij = 0 otherwise.
Find the expected number of visits to six o'clock, starting from six o'clock, before visiting twelve o'clock.