Guassian probability distribution of random walker

See more:

Python2.3

actually, I want gaussian probability distribution from this code so what changes can I do in my code? please suggest me.

What I have tried:

import numpy as np
import matplotlib.pyplot as plt

W = 15 # walkers

X0 = 0

T  = 1   #total time 

dt = .001 #time steps 

N  = int(T/dt) # no of time steps 

D  = 1

np.random.seed(1)

t = dt * np.arange(N)

dx = np.sqrt(2 * D * dt)*np.random.randn(N,W)

x  = np.zeros((N,W))

for w in range(W):
 for i in range(N-1):
    x[i+1][w] = x[i][w] + dx[i][w]

            
        
           
plt.plot(t, x )

plt.show()