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 ε 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 200 experiments and determine how many runs it took to reach the eastern wall. plot the results.