.. _book_fig_chapter3_fig_central_limit:


Example of central limit theorem
--------------------------------
Figure 3.20.

An illustration of the central limit theorem. The histogram in each panel shows
the distribution of the mean value of N random variables drawn from the (0, 1)
range (a uniform distribution with :math:`\mu = 0.5` and W = 1; see eq. 3.39).
The distribution for N = 2 has a triangular shape and as N increases it becomes
increasingly similar to a Gaussian, in agreement with the central limit
theorem. The predicted normal distribution with :math:`\mu = 0.5` and
:math:`\sigma = 1/ \sqrt{12 N}` is shown by the line. Already for N = 10,
the "observed" distribution is essentially the same as the predicted
distribution.



.. image:: ../images/chapter3/fig_central_limit_1.png
    :scale: 100
    :align: center


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