The following code provides the desired output:

``````import numpy as np
import math
import matplotlib.pyplot as plt
random = np.random

P_dis = []

N = 50
# N = the number of iterations i.e. the number of iterations of the loop
# below
T = 1000
allx = np.array([]).reshape(0,T)
ally = np.array([]).reshape(0,T)
allD = np.array([]).reshape(0,T)
allsqrt = np.array([]).reshape(0,T)
for j in range(N):
# T = time steps i.e. the number of jumps the particle makes
x_pos = [0]
y_pos = [0]
# initally empty lists that will be appended below
for i in range(1,T):
A = random.uniform(0 , 1)
B = A * 2 * math.pi
current_x = x_pos[i-1]
current_y = y_pos[i-1]
next_x = current_x + math.cos(B)
# takes previous xpos and applies
next_y = current_y + math.sin(B)
x_pos = x_pos + [next_x]
# appends the next x list with xpos and stores
y_pos = y_pos + [next_y]
sqrt = np.sqrt(i)
dis = np.sqrt((0 - x_pos[T - 1])**2 + (0 - y_pos[T - 1])**2)
dis = np.sqrt((0 - np.array(x_pos))**2 + (0 - np.array(y_pos))**2)
allD = np.vstack([allD,dis])
allx = np.vstack([allx,np.array(x_pos)])
ally = np.vstack([ally,np.array(y_pos)])
allsqrt = np.vstack([allsqrt,dis])
P_dis.append(dis)
print(j)

plt.plot(np.arange(0,T),np.mean(allD,0),'g')
plt.plot(np.arange(0,T),np.sqrt(np.arange(0, T)),'r')
plt.xlabel("N")
plt.ylabel("A")
``````