I am confused on how I would use equation 1.27 (in the screenshot I have attached) to solve this problem. Also what does it mean for the I's to be independent? I am trying to solve Problem 5 in the screenshot.

Problem 5. The simplex method minimizes linear functions by moving between extreme points of a poly- hedral region so that each transition decreases the objective function. Suppose there are n extreme points and they are numbered in increasing order of their values. Consider a Markov chain in which p(1, 1) = 1 and p(i, j) = _T. In other words, when we leave j, we are equally likely to go to any of the extreme points with better value. (1) Use equation (1.27), p. 62, to show that for 2 > 1, we have EiT1 = 1+1/2+ . . . + 1/(i -1). (2) Let I; = 1 if the chain visits j on the way from n to 1. Show that for j 0 for any x E C. If g(a) = 0 for all a E A, and for x E C we have g(x) = 1+p(x, y)8(v) (1.27) Then g(x) = Ex(VA)