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diff --git a/source/know/concept/random-variable/index.md b/source/know/concept/random-variable/index.md
index 1781c8b..ecb8e96 100644
--- a/source/know/concept/random-variable/index.md
+++ b/source/know/concept/random-variable/index.md
@@ -19,50 +19,50 @@ of a random variable.
 
 ## Probability space
 
-A **probability space** or **probability triple** $(\Omega, \mathcal{F}, P)$
+A **probability space** or **probability triple** $$(\Omega, \mathcal{F}, P)$$
 is the formal mathematical model of a given **stochastic experiment**,
 i.e. a process with a random outcome.
 
-The **sample space** $\Omega$ is the set
-of all possible outcomes $\omega$ of the experimement.
-Those $\omega$ are selected randomly according to certain criteria.
-A subset $A \subset \Omega$ is called an **event**,
-and can be regarded as a true statement about all $\omega$ in that $A$.
+The **sample space** $$\Omega$$ is the set
+of all possible outcomes $$\omega$$ of the experimement.
+Those $$\omega$$ are selected randomly according to certain criteria.
+A subset $$A \subset \Omega$$ is called an **event**,
+and can be regarded as a true statement about all $$\omega$$ in that $$A$$.
 
-The **event space** $\mathcal{F}$ is a set of events $A$
+The **event space** $$\mathcal{F}$$ is a set of events $$A$$
 that are interesting to us,
-i.e. we have subjectively chosen $\mathcal{F}$
+i.e. we have subjectively chosen $$\mathcal{F}$$
 based on the problem at hand.
-Since events $A$ represent statements about outcomes $\omega$,
+Since events $$A$$ represent statements about outcomes $$\omega$$,
 and we would like to use logic on those statemenets,
-we demand that $\mathcal{F}$ is a [$\sigma$-algebra](/know/concept/sigma-algebra/).
+we demand that $$\mathcal{F}$$ is a [$$\sigma$$-algebra](/know/concept/sigma-algebra/).
 
-Finally, the **probability measure** or **probability function** $P$
-is a function that maps $A$ events to probabilities $P(A)$.
-Formally, $P : \mathcal{F} \to \mathbb{R}$ is defined to satisfy:
+Finally, the **probability measure** or **probability function** $$P$$
+is a function that maps $$A$$ events to probabilities $$P(A)$$.
+Formally, $$P : \mathcal{F} \to \mathbb{R}$$ is defined to satisfy:
 
-1.  If $A \in \mathcal{F}$, then $P(A) \in [0, 1]$.
-2.  If $A, B \in \mathcal{F}$ do not overlap $A \cap B = \varnothing$,
-    then $P(A \cup B) = P(A) + P(B)$.
-3.  The total probability $P(\Omega) = 1$.
+1.  If $$A \in \mathcal{F}$$, then $$P(A) \in [0, 1]$$.
+2.  If $$A, B \in \mathcal{F}$$ do not overlap $$A \cap B = \varnothing$$,
+    then $$P(A \cup B) = P(A) + P(B)$$.
+3.  The total probability $$P(\Omega) = 1$$.
 
-The reason we only assign probability to events $A$
-rather than individual outcomes $\omega$ is that
-if $\Omega$ is continuous, all $\omega$ have zero probability,
-while intervals $A$ can have nonzero probability.
+The reason we only assign probability to events $$A$$
+rather than individual outcomes $$\omega$$ is that
+if $$\Omega$$ is continuous, all $$\omega$$ have zero probability,
+while intervals $$A$$ can have nonzero probability.
 
 
 ## Random variable
 
-Once we have a probability space $(\Omega, \mathcal{F}, P)$,
-we can define a **random variable** $X$
-as a function that maps outcomes $\omega$
+Once we have a probability space $$(\Omega, \mathcal{F}, P)$$,
+we can define a **random variable** $$X$$
+as a function that maps outcomes $$\omega$$
 to another set, usually the real numbers.
 
 To be a valid real-valued random variable,
-a function $X : \Omega \to \mathbb{R}^n$ must satisfy the following condition,
-in which case $X$ is said to be **measurable**
-from $(\Omega, \mathcal{F})$ to $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$:
+a function $$X : \Omega \to \mathbb{R}^n$$ must satisfy the following condition,
+in which case $$X$$ is said to be **measurable**
+from $$(\Omega, \mathcal{F})$$ to $$(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$$:
 
 $$\begin{aligned}
     \{ \omega \in \Omega : X(\omega) \in B \} \in \mathcal{F}
@@ -70,16 +70,16 @@ $$\begin{aligned}
 \end{aligned}$$
 
 In other words, for a given Borel set
-(see [$\sigma$-algebra](/know/concept/sigma-algebra/)) $B \in \mathcal{B}(\mathbb{R}^n)$,
-the set of all outcomes $\omega \in \Omega$ that satisfy $X(\omega) \in B$
-must form a valid event; this set must be in $\mathcal{F}$.
+(see [$$\sigma$$-algebra](/know/concept/sigma-algebra/)) $$B \in \mathcal{B}(\mathbb{R}^n)$$,
+the set of all outcomes $$\omega \in \Omega$$ that satisfy $$X(\omega) \in B$$
+must form a valid event; this set must be in $$\mathcal{F}$$.
 The point is that we need to be able to assign probabilities
-to statements of the form $X \in [a, b]$ for all $a < b$,
-which is only possible if that statement corresponds to an event in $\mathcal{F}$,
-since $P$'s domain is $\mathcal{F}$.
+to statements of the form $$X \in [a, b]$$ for all $$a < b$$,
+which is only possible if that statement corresponds to an event in $$\mathcal{F}$$,
+since $$P$$'s domain is $$\mathcal{F}$$.
 
-Given such an $X$, and a set $B \subseteq \mathbb{R}$,
-the **preimage** or **inverse image** $X^{-1}$ is defined as:
+Given such an $$X$$, and a set $$B \subseteq \mathbb{R}$$,
+the **preimage** or **inverse image** $$X^{-1}$$ is defined as:
 
 $$\begin{aligned}
     X^{-1}(B)
@@ -87,16 +87,16 @@ $$\begin{aligned}
 \end{aligned}$$
 
 As suggested by the notation,
-$X^{-1}$ can be regarded as the inverse of $X$:
-it maps $B$ to the event for which $X \in B$.
-With this, our earlier requirement that $X$ be measurable
-can be written as: $X^{-1}(B) \in \mathcal{F}$ for any $B \in \mathcal{B}(\mathbb{R}^n)$.
-This is also often stated as "$X$ is *$\mathcal{F}$-measurable"*.
-
-Related to $\mathcal{F}$ is the **information**
-obtained by observing a random variable $X$.
-Let $\sigma(X)$ be the information generated by observing $X$,
-i.e. the events whose occurrence can be deduced from the value of $X$,
+$$X^{-1}$$ can be regarded as the inverse of $$X$$:
+it maps $$B$$ to the event for which $$X \in B$$.
+With this, our earlier requirement that $$X$$ be measurable
+can be written as: $$X^{-1}(B) \in \mathcal{F}$$ for any $$B \in \mathcal{B}(\mathbb{R}^n)$$.
+This is also often stated as "$$X$$ is *$$\mathcal{F}$$-measurable"*.
+
+Related to $$\mathcal{F}$$ is the **information**
+obtained by observing a random variable $$X$$.
+Let $$\sigma(X)$$ be the information generated by observing $$X$$,
+i.e. the events whose occurrence can be deduced from the value of $$X$$,
 or, more formally:
 
 $$\begin{aligned}
@@ -105,29 +105,29 @@ $$\begin{aligned}
     = \{ A \in \mathcal{F} : A = X^{-1}(B) \mathrm{\:for\:some\:} B \in \mathcal{B}(\mathbb{R}^n) \}
 \end{aligned}$$
 
-In other words, if the realized value of $X$ is
-found to be in a certain Borel set $B \in \mathcal{B}(\mathbb{R}^n)$,
-then the preimage $X^{-1}(B)$ (i.e. the event yielding this $B$)
+In other words, if the realized value of $$X$$ is
+found to be in a certain Borel set $$B \in \mathcal{B}(\mathbb{R}^n)$$,
+then the preimage $$X^{-1}(B)$$ (i.e. the event yielding this $$B$$)
 is known to have occurred.
 
-In general, given any $\sigma$-algebra $\mathcal{H}$,
-a variable $Y$ is said to be *"$\mathcal{H}$-measurable"*
-if $\sigma(Y) \subseteq \mathcal{H}$,
-so that $\mathcal{H}$ contains at least
-all information extractable from $Y$.
+In general, given any $$\sigma$$-algebra $$\mathcal{H}$$,
+a variable $$Y$$ is said to be *"$$\mathcal{H}$$-measurable"*
+if $$\sigma(Y) \subseteq \mathcal{H}$$,
+so that $$\mathcal{H}$$ contains at least
+all information extractable from $$Y$$.
 
-Note that $\mathcal{H}$ can be generated by another random variable $X$,
-i.e. $\mathcal{H} = \sigma(X)$.
+Note that $$\mathcal{H}$$ can be generated by another random variable $$X$$,
+i.e. $$\mathcal{H} = \sigma(X)$$.
 In that case, the **Doob-Dynkin lemma** states
-that $Y$ is only $\sigma(X)$-measurable
-if $Y$ can always  be computed from $X$,
-i.e. there exists a function $f$ such that
-$Y(\omega) = f(X(\omega))$ for all $\omega \in \Omega$.
+that $$Y$$ is only $$\sigma(X)$$-measurable
+if $$Y$$ can always  be computed from $$X$$,
+i.e. there exists a function $$f$$ such that
+$$Y(\omega) = f(X(\omega))$$ for all $$\omega \in \Omega$$.
 
 Now, we are ready to define some familiar concepts from probability theory.
-The **cumulative distribution function** $F_X(x)$ is
-the probability of the event where the realized value of $X$
-is smaller than some given $x \in \mathbb{R}$:
+The **cumulative distribution function** $$F_X(x)$$ is
+the probability of the event where the realized value of $$X$$
+is smaller than some given $$x \in \mathbb{R}$$:
 
 $$\begin{aligned}
     F_X(x)
@@ -136,8 +136,8 @@ $$\begin{aligned}
     = P(X^{-1}(]\!-\!\infty, x]))
 \end{aligned}$$
 
-If $F_X(x)$ is differentiable,
-then the **probability density function** $f_X(x)$ is defined as:
+If $$F_X(x)$$ is differentiable,
+then the **probability density function** $$f_X(x)$$ is defined as:
 
 $$\begin{aligned}
     f_X(x)
@@ -147,10 +147,10 @@ $$\begin{aligned}
 
 ## Expectation value
 
-The **expectation value** $\mathbf{E}[X]$ of a random variable $X$
+The **expectation value** $$\mathbf{E}[X]$$ of a random variable $$X$$
 can be defined in the familiar way, as the sum/integral
-of every possible value of $X$ mutliplied by the corresponding probability (density).
-For continuous and discrete sample spaces $\Omega$, respectively:
+of every possible value of $$X$$ mutliplied by the corresponding probability (density).
+For continuous and discrete sample spaces $$\Omega$$, respectively:
 
 $$\begin{aligned}
     \mathbf{E}[X]
@@ -160,18 +160,18 @@ $$\begin{aligned}
     = \sum_{i = 1}^N x_i \: P(X \!=\! x_i)
 \end{aligned}$$
 
-However, $f_X(x)$ is not guaranteed to exist,
+However, $$f_X(x)$$ is not guaranteed to exist,
 and the distinction between continuous and discrete is cumbersome.
-A more general definition of $\mathbf{E}[X]$
+A more general definition of $$\mathbf{E}[X]$$
 is the following Lebesgue-Stieltjes integral,
-since $F_X(x)$ always exists:
+since $$F_X(x)$$ always exists:
 
 $$\begin{aligned}
     \mathbf{E}[X]
     = \int_{-\infty}^\infty x \dd{F_X(x)}
 \end{aligned}$$
 
-This is valid for any sample space $\Omega$.
+This is valid for any sample space $$\Omega$$.
 Or, equivalently, a Lebesgue integral can be used:
 
 $$\begin{aligned}
@@ -182,8 +182,8 @@ $$\begin{aligned}
 An expectation value defined in this way has many useful properties,
 most notably linearity.
 
-We can also define the familiar **variance** $\mathbf{V}[X]$
-of a random variable $X$ as follows:
+We can also define the familiar **variance** $$\mathbf{V}[X]$$
+of a random variable $$X$$ as follows:
 
 $$\begin{aligned}
     \mathbf{V}[X]