Minor changes

source/statistics/bessel_correction.rst

@@ -0,0 +1,4 @@
+Bessel's Correction
+-----------------------
+
+TODO

source/statistics/degree_of_freedom.rst

@@ -1,4 +0,0 @@
-Degree of Freedom
-===================
-
-BAM

source/statistics/index.rst

@@ -6,6 +6,6 @@ Statistics
    :maxdepth: 2
 
    metrics
-   degree_of_freedom
+   bessel_correction
 
 Statistics notes.

source/statistics/metrics.rst

@@ -70,3 +70,32 @@ Output example:
    ----- Experiment 3 -----
    Means SD: 1.27
    SEM       1.26
+
+Degree of Freedom
+--------------------
+
+The degree of freedom is a quantity defined for a given computation.
+It corresponds to the number of parameters that are allowed to vary in that computation.
+In other words, how many varying values are contributing to the computation.
+For example, when computing the mean of a random variable :math:`X={x_1,...,x_n}`, there are :math:`n` parameters
+that are allowed to change in the following formula:
+
+.. math::
+   \overline{x}=\frac{\sum_{i=1}^n x_i}{n}
+
+Thus, the degree of freedom in this computation is :math:`n`.
+When computing the standard deviation of :math:`X`, we have:
+
+.. math::
+  \hat{\sigma}_x=\frac{\sum_{i=0}^n (x_i-\overline{x})^2}{n}
+
+In this case, the degree of freedom is :math:`n-1`. As the mean is already known, only :math:`n-1`
+of the :math:`x_i` are allowed to vary. By knowing :math:`n-1` of the :math:`x_i`, we can deduce the last
+one as follow:
+
+.. math::
+   \overline{x}=\frac{(\sum_{i=1}^{n-1} x_i) + x_n}{n} \Longrightarrow x_n = n\overline{x} - (\sum_{i=1}^{n-1} x_i)
+
+
+
+