Var(x) and cov(x, x) don't give the same result in numpy

Question

A property of the covariance is, that cov(x, x) = var(x)

However, in numpy I don't get the same result.

from numpy import var, cov

x = range(10)
y = var(x)
z = cov(x, x)[0][1]
print y, z

Am I doing something wrong here? How can I obtain the correct result?

Answer 1

The default ddof of cov (None) and var (0) are different. Try specifying the ddof (or bias):

>>> cov(x, x, ddof=0)
array([[ 8.25,  8.25],
       [ 8.25,  8.25]])
>>> var(x)
8.25

Answer 2

You must use z=cov(x,bias=1) in order to normalize by N ,because var is also norm by N (according to this