diff --git a/source/statistics/bayes_theorem.rst b/source/statistics/bayes_theorem.rst
index 4e19a3b..8d310f4 100644
--- a/source/statistics/bayes_theorem.rst
+++ b/source/statistics/bayes_theorem.rst
@@ -1,7 +1,7 @@
 Bayes' Theorem
 ---------------
 
-This page is inpired from:
+This page is inspired from:
 
 * `MathIsFun <https://www.mathsisfun.com/data/bayes-theorem.html>`__
 * `Wikipedia <https://en.wikipedia.org/wiki/Bayes%27_theorem>`__
@@ -11,8 +11,8 @@ Theorem
 
 The Bayes's theorem describes the probability of an event, based on prior knowledge of conditions
 that might be related to the event.
-To compute :math:`P(A|B)`, in other words, the probability of the event :math:`A` to happen, knowing that :math:`B`
-already happen, the following drawing can be used:
+To compute :math:`P(A|B)`, in other words, the probability of the event :math:`A` to happend, knowing that :math:`B`
+already happend, the following drawing can be used:
 
 .. image:: figures/bayes_theorem.svg
     :align: center
@@ -20,7 +20,7 @@ already happen, the following drawing can be used:
 
 |
 
-The red area represents :math:`P(B)=a3+a4`. Thus, to compute :math:`P(A|B)` we do:
+The red area represents :math:`P(B)=a3+a4`. To compute :math:`P(A|B)` we do:
 
 .. math::
    P(A|B)=\frac{a3}{a3+a4}=\frac{P(A)P(B|A)}{P(A)P(B|A)+P(\neg A)P(B|\neg A)}=\frac{P(A)P(B|A)}{P(B)}
@@ -68,4 +68,4 @@ Let's draw the little diagram:
 
    &=\frac{0.01 \times 0.80}{0.01 \times 0.80 + 0.99 \times 0.10} = 0.0747
 
-The chances that Anna really has Allergy is about 7%.
+The chances that Anna really has allergy is about 7%.
diff --git a/source/statistics/bessel_correction.rst b/source/statistics/bessel_correction.rst
index 4719331..be1bbb4 100644
--- a/source/statistics/bessel_correction.rst
+++ b/source/statistics/bessel_correction.rst
@@ -8,7 +8,8 @@ Bessel's Correction
 Bessel's correction is the use of :math:`n-1` instead of :math:`n` in the formulas for sample
 variance and sample standard deviation.
 In fact, using :math:`n` as a denominator leads to a biased estimator.
-This variance estimator is noted :math:`s^2_n`.
+The biased estimator for the sample standard deviation is noted :math:`s_n`.
+The biased estimator for the sample variance is noted :math:`s^2_n`.
 Lets compute the discrepency between population variance and the biased sample variance:
 
 .. math::
@@ -33,9 +34,9 @@ Lets compute the discrepency between population variance and the biased sample v
    &= \frac{\sigma^2}{n}
 
 
-This result shows us that the discrepency between the population and sample variance is :math:`\frac{\sigma^2}{n}`.
+This result shows that the discrepency between the population and sample variance is :math:`\frac{\sigma^2}{n}`.
 It is simply, the :ref:`Standard Error of the Mean <SEM>`.
-From this result we can deduce how :math:`S_n^2` must be adjusted:
+From this result we can deduce how :math:`s_n^2` must be adjusted to be unbiased:
 
 .. math::
    \mathbb{E} \left[ s^2_n \right] = \sigma^2 - \frac{\sigma^2}{n} = \frac{n-1}{n} \sigma^2
diff --git a/source/statistics/probability_distribution_functions.rst b/source/statistics/probability_distribution_functions.rst
index c2425ed..370152e 100644
--- a/source/statistics/probability_distribution_functions.rst
+++ b/source/statistics/probability_distribution_functions.rst
@@ -6,7 +6,7 @@ Probability Distribution Functions
 Probability Density Function
 =============================
 
-The Probability Density Function (PDF) is function defined for a random variable :math:`X` such that:
+The Probability Density Function (PDF) is a function defined for a random variable :math:`X` such that:
 
 .. math::
    \forall (a,b) \in \mathbb{R}^2,\, P(a \le X \le b) = \int_a^b f_X(x)dx
@@ -16,7 +16,7 @@ Properties:
 #. :math:`\int_{-\infty}^{+\infty} f_X(x)dx=1`
 #. :math:`P(X=a)=\int_{a}^{a} f_X(x)dx=0`
 
-From property *2* it can be derived that (`source <http://yallouz.arie.free.fr/terminale_cours/probascont/prob-continue.php>`__):
+From *property 2*, it can be derived that (`source <http://yallouz.arie.free.fr/terminale_cours/probascont/prob-continue.php>`__):
 
 .. math::
    P(a \le X \le b) &= P(a < X \le b) =P(a \le X < b) =P(a < X < b)