Suppose we have n points in a circle with 1 person at each point. If every person randomly moves either left or right to one of their direct neighbors, what is the expected number of empty points in the circle after everyone moves?
I'm having some trouble figuring out exactly how to go about solving this problem. My current thought process is that the neighbors of every person have to make a certain choice for a point to be empty, but I can't put this into a formula. I feel that indicator random variables could help.
I'm having some trouble figuring out exactly how to go about solving this problem. My current thought process is that the neighbors of every person have to make a certain choice for a point to be empty, but I can't put this into a formula. I feel that indicator random variables could help.