added 3 definitions

Author: JoramSoch

D/mom-cent.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-10-08 03:37:00
+
+title: "Central moment"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Further moments"
+definition: "Central moment"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Moment (mathematics)"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-10-08"
+    url: "https://en.wikipedia.org/wiki/Moment_(mathematics)#Significance_of_the_moments"
+
+def_id: "D98"
+shortcut: "mom-cent"
+username: "JoramSoch"
+---
+
+
+**Definition:** Let $X$ be a [random variable](/D/rvar) with [expected value](/D/mean) $\mu$ and let $n$ be a positive integer. Then, the $n$-th central moment of $X$ is defined as the $n$-th [moment](/D/mom) of $X$ about the value $\mu$:
+
+$$ \label{eq:mom-cent}
+\mu_n = \mathrm{E}[(X-\mu)^n] \; .
+$$

D/mom-raw.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-10-08 03:31:00
+
+title: "Raw moment"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Further moments"
+definition: "Raw moment"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Moment (mathematics)"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-10-08"
+    url: "https://en.wikipedia.org/wiki/Moment_(mathematics)#Significance_of_the_moments"
+
+def_id: "D97"
+shortcut: "mom-raw"
+username: "JoramSoch"
+---
+
+
+**Definition:** Let $X$ be a [random variable](/D/rvar) and let $n$ be a positive integer. Then, the $n$-th raw moment of $X$, also called ($n$-th) "crude moment", is defined as the $n$-th [moment](/D/mom) of $X$ about the value 0:
+
+$$ \label{eq:mom-raw}
+\mu_n' = \mu_n(0) = \mathrm{E}[(X-0)^n] = \mathrm{E}[X^n] \; .
+$$

D/mom-stand.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-10-08 03:47:00
+
+title: "Standardized moment"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Further moments"
+definition: "Standardized moment"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Moment (mathematics)"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-10-08"
+    url: "https://en.wikipedia.org/wiki/Moment_(mathematics)#Standardized_moments"
+
+def_id: "D99"
+shortcut: "mom-stand"
+username: "JoramSoch"
+---
+
+
+**Definition:** Let $X$ be a [random variable](/D/rvar) with [expected value](/D/mean) $\mu$ and [standard deviation](/D/std) $\sigma$ and let $n$ be a positive integer. Then, the $n$-th standardized moment of $X$ is defined as the $n$-th [moment](/D/mom) of $X$ about the value $\mu$, divided by the $n$-th power of $\sigma$:
+
+$$ \label{eq:mom-stand}
+\mu_n^{*} = \frac{\mu_n}{\sigma^n} =  \frac{\mathrm{E}[(X-\mu)^n]}{\sigma^n} \; .
+$$