Guassian probability distribution of random walker

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Python2.3

actually, I want a gaussian probability distribution curve. so what changes do I have to make in my code for this? please correct my code if anyone has an idea about it. thank you

What I have tried:

#set up the data we will needed
import numpy as np
import matplotlib.pyplot as plt

W = 20 # walkers

X0 = 0

T  = 1   #total time 

dt = .001 #time steps 

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

D  = 1

np.random.seed(10)

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()