uniform_point_generation.py

import numpy as np
from numpy.random import uniform as unif

def euclidean_dist(x,y):
        return np.sqrt(sum((x-y)**2))

def method1(n, N = 10000):
    
    dist = 0
    for i in range(N):
        x = np.array([unif(0,1) for i in range(n)])
        y = np.array([unif(0,1) for i in range(n)])
        dist = (dist*i + euclidean_dist(x,y))/(i+1.0)
    
    return dist

def method2(n, N = 10000):
    dist = 0
    for i in range(N):
        x = unif(0,1,n)
        y = unif(0,1,n)
        dist = (dist*i + euclidean_dist(x,y))/(i+1.0)
    
    return dist

d1 = []
d2 = []
for i in range(100):
    d1.append(method1(2))
    d2.append(method2(2))

print ('d1', np.average(d1), np.std(d1))
print ('d2', np.average(d2), np.std(d2))