corrected some pages

Several small mistakes/errors were corrected in several proofs/definitions.

Author: JoramSoch

D/pgf.md

@@ -29,18 +29,18 @@ username: "JoramSoch"
 
 **Definition:**
 
-1) If $X$ is a discrete [random variable](/D/rvar) taking values in the non-negative integers $\left\lbrace 0, 1, \ldots \right\rbrace$, then the probability-generating function of $X$ is defined as
+1) If $X$ is a [discrete](/D/rvar-disc) [random variable](/D/rvar) taking values in the non-negative integers $\left\lbrace 0, 1, \ldots \right\rbrace$, then the probability-generating function of $X$ is defined as
 
 $$ \label{eq:pgf-var}
-G_X(z) = \mathrm{E} \left[ z^X \right] = \sum_{x=0}^{\infty} p(x) \, z^x
+G_X(z) = \sum_{x=0}^{\infty} p(x) \, z^x
 $$
 
 where $z \in \mathbb{C}$ and $p(x)$ is the [probability mass function](/D/pmf) of $X$.
 
-2) If $X$ is a discrete [random vector](/D/rvec) taking values in the $n$-dimensional integer lattice $x \in \left\lbrace 0, 1, \ldots \right\rbrace^n$, then the probability-generating function of $X$ is defined as
+2) If $X$ is a [discrete](/D/rvar-disc) [random vector](/D/rvec) taking values in the $n$-dimensional integer lattice $x \in \left\lbrace 0, 1, \ldots \right\rbrace^n$, then the probability-generating function of $X$ is defined as
 
 $$ \label{eq:cgf-vec}
-G_X(z) = \mathrm{E} \left[ {z_1}^{X_1} \cdot \ldots \cdot {z_n}^{X_n} \right] = \sum_{x_1=0}^{\infty} \cdots \sum_{x_n=0}^{\infty} p(x_1,\ldots,x_n) \, {z_1}^{x_1} \cdot \ldots \cdot {z_n}^{x_n}
+G_X(z) = \sum_{x_1=0}^{\infty} \cdots \sum_{x_n=0}^{\infty} p(x_1,\ldots,x_n) \, {z_1}^{x_1} \cdot \ldots \cdot {z_n}^{x_n}
 $$
 
 where $z \in \mathbb{C}^n$ and $p(x)$ is the [probability mass function](/D/pmf) of $X$.

P/mean-prodsqr.md

@@ -11,7 +11,7 @@ title: "Square of expectation of product is less than or equal to product of exp
 chapter: "General Theorems"
 section: "Probability theory"
 topic: "Expected value"
-theorem: "Squared expectation of product"
+theorem: "Squared expectation of a product"
 
 sources:
   - authors: "ProofWiki"