corrected some pages

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

Author: JoramSoch

D/cvlme.md

@@ -48,16 +48,16 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let there be a [data set](/D/data) $y$ with mutually exclusive and collectively exhaustive subsets $y_1, \ldots, y_S$. Assume a [generative model](/D/gm) $m$ with model parameters $\theta$ implying a [likelihood function](/D/lf) $p(y \vert \theta, m)$ and a [non-informative](/D/prior-inf) [prior density](/D/prior) $p(\theta \vert m)$.
+**Definition:** Let there be a [data set](/D/data) $y$ with mutually exclusive and collectively exhaustive subsets $y_1, \ldots, y_S$. Assume a [generative model](/D/gm) $m$ with model parameters $\theta$ implying a [likelihood function](/D/lf) $p(y \vert \theta, m)$ and a [non-informative](/D/prior-inf) [prior density](/D/prior) $p_{\mathrm{ni}}(\theta \vert m)$.
 
 Then, the cross-validated log model evidence of $m$ is given by
 
 $$ \label{eq:cvLME}
 \mathrm{cvLME}(m) = \sum_{i=1}^{S} \log \int p( y_i \vert \theta, m ) \, p( \theta \vert y_{\neg i}, m ) \, \mathrm{d}\theta
 $$
 
-where $y_{\neg i} = \bigcup_{j \neq i} y_j$ is the union of all data subsets except $y_i$ and $p( \theta \vert y_{\neg i}, m )$ is the [posterior distribution](/D/post) obtained from $y_{\neg i}$ when using the [prior distribution](/D/prior) $p(\theta \vert m)$:
+where $y_{\neg i} = \bigcup_{j \neq i} y_j$ is the union of all data subsets except $y_i$ and $p( \theta \vert y_{\neg i}, m )$ is the [posterior distribution](/D/post) obtained from $y_{\neg i}$ when using the [prior distribution](/D/prior) $p_{\mathrm{ni}}(\theta \vert m)$:
 
 $$ \label{eq:post}
-p( \theta \vert y_{\neg i}, m ) = \frac{p( y_{\neg i} \vert \theta, m ) \, p(\theta \vert m)}{p( y_{\neg i} \vert m )} \; .
+p( \theta \vert y_{\neg i}, m ) = \frac{p( y_{\neg i} \vert \theta, m ) \, p_{\mathrm{ni}}(\theta \vert m)}{p( y_{\neg i} \vert m )} \; .
 $$

D/rvar-uni.md

@@ -29,6 +29,8 @@ username: "JoramSoch"
 
 **Definition:** Let $X$ be a [random variable](/D/rvar) with possible outcomes $\mathcal{X}$. Then,
 
+* $X$ is called a two-valued random variable or [random event](/D/reve), if $\mathcal{X}$ has two elements, e.g. $\mathcal{X} = \left\lbrace \mathrm{true}, \mathrm{false} \right\rbrace$ or $\mathcal{X} = \left\lbrace 1, 0 \right\rbrace$;
+
 * $X$ is called a univariate random variable or [random scalar](/D/rvar), if $\mathcal{X}$ is one-dimensional, i.e. (a subset of) the real numbers $\mathbb{R}$;
 
 * $X$ is called a multivariate random variable or [random vector](/D/rvec), if $\mathcal{X}$ is multi-dimensional, e.g. (a subset of) the $n$-dimensional Euclidean space $\mathbb{R}^n$;

P/beta-cdf.md

@@ -14,6 +14,12 @@ topic: "Beta distribution"
 theorem: "Cumulative distribution function"
 
 sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Beta distribution"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-11-19"
+    url: "https://en.wikipedia.org/wiki/Beta_distribution#Cumulative_distribution_function"
   - authors: "Wikipedia"
     year: 2020
     title: "Beta function"

P/chi2-pdf.md

@@ -39,7 +39,7 @@ $$ \label{eq:chi2}
 Y \sim \chi^{2}(k) \; .
 $$
 
-Then, the [probability density function](/D/pdf) of $X$ is
+Then, the [probability density function](/D/pdf) of $Y$ is
 
 $$ \label{eq:chi2-pdf}
 f_Y(y) = \frac{1}{2^{k/2} \, \Gamma (k/2)} \, y^{k/2-1} \, e^{-y/2} \; .