2D Square Lattice Random Walker Problem Mean Displacement Vectors

The Question is asking to compute the mean displacement vector by ensemble averaging xN and yN over the M random walks, for different values of N. Plot as a function of N and then the mean squre displacement by ensemble averaging R_N^2 for M-1000 walkers who are all originally at the origin in two-d.

Here is my coder to put the maps of serval independent random walks:

import numpy as np
import pylab 
import random 

# defining the number of steps 
M = 1000

#creating two array for containing x and y coordinate 
#of size equals to the number of size and filled up with 0's 
x = np.zeros(M) 
y = np.zeros(M) 

# filling the coordinates with random variables

for i in range(1, M):
      value = random.randint(1, 4)
      if value == 1:
           x[i] = x[i - 1] + 1
           y[i] = y[i - 1] 
      elif value == 2: 
           x[i] = x[i - 1] - 1
           y[i] = y[i - 1] 
      elif value == 3: 
           x[i] = x[i - 1] 
           y[i] = y[i - 1] + 1
      else: 
           x[i] = x[i - 1] 
           y[i] = y[i - 1] - 1


def compute_SquareMean(value):
   totalsize=len(value)
   msd=[]
  for i in range(totalsize-1):
      j=i+1
      msd.append(np.sum((value[0:-j]      

value[j::])**2)/float(totalsize-j)) msd=np.array(msd) return msd

print(compute_SquareMean)
pylab.title("Random Walk ($n = " + str(M) + "$ steps)") 
pylab.plot(x,y)      
pylab.show() 

Can someone show me the code to compute the mean displacement vector by ensemble averaging xN and yN over the M random walks, for different values of N and the mean squre displacement by ensemble averaging R_N^2. I suspect my compute_SquareMean function is not working properly because it is giving a location as the output. It should be noted that the for loop for the random walker path is working perfectly. Thank you