Question: (i) Write a function to simulate a random walk in the plane that moves up, down, left, and right with equal probability. Use your function

(i) Write a function to simulate a random walk in the plane that moves up, down, left, and right with equal probability. Use your function to estimate the average distance from the origin after n = 1000 steps.

(ii) Modify your function to simulate a three-dimensional random walk that moves in one of six directions with equal probability. Estimate the average distance from the origin after n = 1000 steps.

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