A particle moves along the following graph so that at each step it is equally likely to move to any of its neighbors 2 (n-1) Starting at 0 show that the expected number of steps it takes to reach n is n. (Hint Let T, denote the number of steps it takes to go from vertex i - 1 to vertex i, i = 1,..., n Determine E[T] recursively, first for i = 1, then i = 2, and so on.)