Question: A random walk in two dimensions is the following game played on the x-J coordinate system. Starting at the origin, (0, 0). each iteration consists of a random step either 1 unit left, up, right, or down. The walk terminates when the walker returns to the origin. The probability of this happening is 1 in two dimensions but less than I in three dimensions.) Write a program that performs 100 independent random walks and computes the average number of steps taken in each direction.