The main part of the program below consists of two loops: each time around the outer loop over the number of trials we reset $\phi_0$ and the array of path positions, `pos`

and conduct the random walk over $n$ steps (the inner loop). If, after a walk, we are within one unit of the end position, B, we add that walk to the average, plot it, and increment the counter for completed walks, `ngood`

. Finally, we divide our accumulated paths by `ngood`

to find the average path and plot that.

```
import numpy as np
import pylab
# Random walk from a = (0,0) to b = (b, 0)
b = 10
# Set off each time at an angle phi0 from the a-b direction
phi0 = np.radians(110)
# Take a total of 40 steps
n = 40
# At each step, change phi by a random amount selected from a normal
# distribution with standard deviation sigma
sigma = np.radians(17)
# Conduct a total of ntrials walks
ntrials = 1000000
av = np.zeros((n, 2))
ngood = 0
for j in range(ntrials):
phi = phi0
pos = np.zeros((n, 2))
for i in range(1, n):
dx, dy = np.cos(phi), np.sin(phi)
pos[i] = pos[i-1] + (dx, dy)
phi += sigma * np.random.randn()
if np.hypot(b-pos[-1,0], pos[-1,1]) < 1.:
pylab.plot(pos[:,0], pos[:,1], color='b')
av += pos
ngood += 1
print(j)
av /= ngood
pylab.plot(av[:,0], av[:,1], lw=3, color='r')
pylab.show()
```

A typical output is shown below.