Write a function randomWalk ( ...) which simulates one path (or trajectory) of a simple symmetric random walk with 2N time steps (i. e. from 0,1,2, ...,2N) starting at?0=0.

Input: lengthOfRandomWalk = 2N

Output: samplePath: Array of length 2N+1 with the entire path of the random walk on 0,1,2, ...,2N

import numpy as np

import random

import matplotlib. pyplot as plt

def randomWalk (L):

# S is a 2d array where x = row1 = S[0][:], y = row2 = S[1][:]

S = np. zeros (shape = (2, L+1))

directions = [1,2,3,4]

for i in range (1, L+1):

direction = np. random. choice (directions)

if direction = = 1:

S[0][i] = S[0][i-1] + 1; S[1][i] = S[1][i-1] # go right

elif direction = = 2:

S[0][i] = S[0][i-1] - 1; S[1][i] = S[1][i-1] # go left

elif direction = = 3:

S[0][i] = S[0][i-1]; S[1][i] = S[1][i-1] + 1 # go up

else:

S[0][i] = S[0][i-1]; S[1][i] = S[1][i-1] - 1; # go down

samplePath = S

return samplePath

n = 100;

path = randomWalk (2*n)

print (path)

x = path[0][:]; y = path[1][:];

plt. figure (1)

plt. plot (x, y,'-')

plt. ylabel ('y')

plt. xlabel ('x')

plt. show ()