A particle moves in the plane according to a two-dimensional symmetric random walk (see p. 75). That is, the particle has a probability equal to 1/4 of moving from its current position, (Xn,Fn), to any of its four nearest a neighbors. We suppose that the particle is at the origin at time n = 0, so that XQ = YQ - 0. Thus, at time n = 1, the particle will be in one of the following states: (0,1), (0,-1), (1,0), or (-1,0). Let
be the square of the distance of the particle from the origin at time n. Calculate 