added 2 definitions

Author: JoramSoch

D/max.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-11-12 05:33:00
+
+title: "Maximum"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Further summary statistics"
+definition: "Maximum"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Sample maximum and minimum"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-11-12"
+    url: "https://en.wikipedia.org/wiki/Sample_maximum_and_minimum"
+
+def_id: "D108"
+shortcut: "max"
+username: "JoramSoch"
+---
+
+
+**Definition:** The maximum of a sample or random variable is its highest observed or possible value.
+
+<br>
+1) Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ be a [sample](/D/samp) from a [random variable](/D/rvar) $X$. Then, the maximum of $x$ is
+
+$$ \label{eq:max-samp}
+\mathrm{max}(x) = x_j, \quad \text{such that} \quad x_j \geq x_i \quad \text{for all} \quad i = 1, \ldots, n, \; i \neq j \; ,
+$$
+
+i.e. the maximum is the value which is larger than or equal to all other observed values.
+
+<br>
+2) Let $X$ be a [random variable](/D/rvar) with possible values $\mathcal{X}$. Then, the maximum of $X$ is
+
+$$ \label{eq:max-rvar}
+\mathrm{max}(X) = \tilde{x}, \quad \text{such that} \quad \tilde{x} > x \quad \text{for all} \quad x \in \mathcal{X}\setminus\left\lbrace \tilde{x} \right\rbrace \; ,
+$$
+
+i.e. the maximum is the value which is larger than all other possible values.

D/min.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-11-12 05:25:00
+
+title: "Minimum"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Further summary statistics"
+definition: "Minimum"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Sample maximum and minimum"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-11-12"
+    url: "https://en.wikipedia.org/wiki/Sample_maximum_and_minimum"
+
+def_id: "D107"
+shortcut: "min"
+username: "JoramSoch"
+---
+
+
+**Definition:** The minimum of a sample or random variable is its lowest observed or possible value.
+
+<br>
+1) Let $x = \left\lbrace x_1, \ldots, x_n \right\rbrace$ be a [sample](/D/samp) from a [random variable](/D/rvar) $X$. Then, the minimum of $x$ is
+
+$$ \label{eq:min-samp}
+\mathrm{min}(x) = x_j, \quad \text{such that} \quad x_j \leq x_i \quad \text{for all} \quad i = 1, \ldots, n, \; i \neq j \; ,
+$$
+
+i.e. the minimum is the value which is smaller than or equal to all other observed values.
+
+<br>
+2) Let $X$ be a [random variable](/D/rvar) with possible values $\mathcal{X}$. Then, the minimum of $X$ is
+
+$$ \label{eq:min-rvar}
+\mathrm{min}(X) = \tilde{x}, \quad \text{such that} \quad \tilde{x} < x \quad \text{for all} \quad x \in \mathcal{X}\setminus\left\lbrace \tilde{x} \right\rbrace \; ,
+$$
+
+i.e. the minimum is the value which is smaller than all other possible values.