In a two-dimensional symmetric random walk starting at the origin the probability that the nth step takes

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In a two-dimensional symmetric random walk starting at the origin the probability that the nth step takes the particle to (x, y) is (27)-22-n *[*[* (cos x + cos f)" + cos xx cos y da

d. Verify this formula and find the analogue for three dimensions. (Hint: Check that the expression satisfies the proper difference equation.)

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