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
neighbors. We suppose that the particle is at the origin at time n = 0, so thatXQ = 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
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