(10 Points) (A random walk on a circle) The integers 1, 2, ..., N are labeled on a circle in a counter-clockwise order.
Posted: Sun Oct 03, 2021 3:31 pm
- 10 Points A Random Walk On A Circle The Integers 1 2 N Are Labeled On A Circle In A Counter Clockwise Order 1 (30.13 KiB) Viewed 137 times
(10 Points) (A random walk on a circle) The integers 1, 2, ..., N are labeled on a circle in a counter-clockwise order. (When N 12, numbering on the face of an old clock represents this.) Consider a random walk (Xn) on the state space {1,2, ...,N}. Its one-step transition probabilities are p(i,i+1) =p for 1 <i<N-1, pſi, i -1)=1-p for 2<i<N, P(N, 1) =p, and p(1,1)=1-p, where pe (0,1). Compute P[(X.) visits every other state before returning to 1 |X0 = 1).