%pylab inline
import random 
import matplotlib.pyplot as plt

n = 10
k = 10
x = []
y = []

for i in range(n):
    x.append(random.random())
    y.append(random.random())
    
part = 1. / k
x.sort()
y.sort()
numInPartsX = [0 for i in range(k)]
numInPartsY = [0 for i in range(k)]
j = 0
step = part

print x
print
print y

def gist(x, numInParts, part):
    j = 0
    step = part
    for i in x:
        while 1:
            if i < step:
                numInParts[j] += 1.
                break
            else:
                j += 1
                step += part
    return numInParts
                
print gist(x, numInPartsX, part)
print
print gist(y, numInPartsY, part)

x2 = 0.
for i in range(k):
    if numInPartsY[i] != 0:
        x2 += (numInPartsX[i] / k - numInPartsY[i] / k) ** 2 / numInPartsY[i]

print x2
print x2 * k