Consider a particle in a room. how likely is the particle to hit the east wall of the room? assume the western wall repels the particles and there is no vertical motion. the position at a subsequent time is related to the current position by x^n + 1 = x^n +f(x^n)+ noise where f(x) = k/x^2 so that the force away from the western wall at x = 0 is proportional to the inverse of the distance squared.

the noise is given by epsilon times a random number between minus one and one. the eastern wall is taken to be at x = 5 and the constant of proportionality for the repulsive force is k = 0.5, with a noise amplitude of 1. run at least 2(h) experiments and determine how many runs it took to reach the eastern wall. plot the results.