displaystyle - Moozonian Omega

${\begin{array}{rrcl}F:&\mathbb {R} &\rightarrow &\mathbb {R} \\&x&\mapsto &\displaystyle \Phi \left({\frac {x-\mu }{\sigma }}\right)={\frac {1}{2}}+{\frac {1}{\sqrt {2\pi }}}\cdot \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!\cdot 2^{n}\cdot \sigma ^{2n+1}}}\cdot {\frac {(z-\mu )^{2n+1}}{2n+1}}\\&&&=\displaystyle {\frac {1}{2}}+{\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\cdot \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!\cdot (2\cdot \sigma ^{2})^{n}}}\cdot {\frac {(z-\mu )^{2n+1}}{2n+1}}\end{array}}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

${\begin{array}{rcl}f(z)&=&\displaystyle {\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\cdot e^{-{\frac {(z-\mu )^{2}}{2\sigma ^{2}}}},\ \ \ -\infty <x<+\infty \\&=&\displaystyle {\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\cdot \sum _{n=0}^{\infty }{\frac {1}{n!}}\cdot \left({\frac {-1}{2\cdot \sigma ^{2}}}\right)^{n}\cdot (x-\mu )^{2n}\\\end{array}}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

${\begin{array}{rcl}F(x)&=&\displaystyle {\frac {1}{\sigma {\sqrt {2\pi }}}}\int _{-\infty }^{x}e^{-{\frac {1}{2}}\left({\frac {t-\mu }{\sigma }}\right)^{2}}\mathrm {d} t,\quad x\in \mathbb {R} \\&=&\displaystyle {\frac {1}{2}}+{\frac {1}{\sigma {\sqrt {2\pi }}}}\cdot \sum _{n=0}^{\infty }{\frac {1}{n!\cdot (2n+1)}}\cdot \left({\frac {-1}{2\cdot \sigma ^{2}}}\right)^{n}\cdot (z-\mu )^{2n+1}\end{array}}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

$h(k\mid 52;4;5):=P(X=k)={\frac {\displaystyle {4 \choose k}{52-4 \choose 5-k}}{\displaystyle {52 \choose 5}}}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Varianz (Stochastik) – Wikipedia

${\displaystyle D_{\text{KL}}(P\parallel Q)}$

Sensitive Content Hidden
Turn off Family Mode to view

en.wikipedia.org

Visit

{\displaystyle {\displaystyle D_{\text{KL}}(P\p...

${\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}$

Sensitive Content Hidden
Turn off Family Mode to view

sl.wikipedia.org

Visit

Normalna porazdelitev - Wikipedija, prosta enci...

$\displaystyle {\bar {X}}={\frac {\sum _{i=1}^{n}X_{i}}{n}}$

Sensitive Content Hidden
Turn off Family Mode to view

it.wikipedia.org

Visit

Distribuzione normale - Wikipedia

${\displaystyle {\frac {1}{2}}\log(2\pi \sigma ^{2})+{\frac {1}{2}}}$

Sensitive Content Hidden
Turn off Family Mode to view

el.wikipedia.org

Visit

Κανονική κατανομή - Βικιπαίδεια

$f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}\mathrm {e} ^{\displaystyle -{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}};-\infty <x<\infty$

Sensitive Content Hidden
Turn off Family Mode to view

eu.wikipedia.org

Visit

Banaketa normal - Wikipedia, entziklopedia askea.

${\begin{array}{rrcl}\Phi :&\mathbb {R} &\rightarrow &\mathbb {R} \\&x&\mapsto &\displaystyle {\frac {1}{2}}+{\widehat {\Phi }}(x)={\frac {1}{2}}+{\frac {1}{\sqrt {2\pi }}}\cdot \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!\cdot 2^{n}}}\cdot {\frac {z^{2n+1}}{2n+1}}\end{array}}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

${\begin{array}{rrcl}{\widehat {\Phi }}_{r}:&{\overline {D_{r}(0)}}&\rightarrow &\mathbb {C} \\&x&\mapsto &\displaystyle {\widehat {\Phi }}_{r}(x)={\frac {1}{\sqrt {2\pi }}}\cdot \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!\cdot 2^{n}}}\cdot {\frac {z^{2n+1}}{2n+1}}\end{array}}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

${\begin{array}{rrcl}\varphi _{n}:&\mathbb {C} &\rightarrow &\mathbb {C} \\&x&\mapsto &\displaystyle \varphi _{n}(x)=\sum _{k=0}^{n}{\frac {(-1)^{k}}{k!\cdot 2^{k}}}\cdot z^{2k}\end{array}},$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

${\begin{array}{rrcl}\varphi :&\mathbb {C} &\rightarrow &\mathbb {C} \\&z&\mapsto &\displaystyle \varphi (z)={\frac {1}{\sqrt {2\pi }}}\cdot e^{-{\frac {z^{2}}{2}}}={\frac {1}{\sqrt {2\pi }}}\cdot \underbrace {\sum _{n=0}^{\infty }{\frac {(-1)^{n}}{n!\cdot 2^{n}}}\cdot z^{2n}} _{=e^{-{\frac {z^{2}}{2}}}}\end{array}}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

$F(x)={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{x}e^{-{\frac {1}{2}}t^{2}}\mathrm {d} t=\displaystyle {\frac {1}{2}}+{\frac {1}{\sqrt {2\pi }}}\cdot \sum _{n=0}^{\infty }{\frac {1}{n!\cdot (2n+1)}}\cdot \left({\frac {-1}{2}}\right)^{n}\cdot x^{2n+1},\quad x\in \mathbb {R}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

${\begin{array}{rrcl}{\widehat {F}}:&D_{r}(0)&\rightarrow &\mathbb {C} \\&z&\mapsto &\displaystyle {\widehat {F}}(x)=\sum _{k=0}^{\infty }{\frac {1}{n!\cdot (2n+1)}}\cdot \left({\frac {-1}{2\cdot \sigma ^{2}}}\right)^{n}\cdot (x-\mu )^{2n+1}\end{array}}_{.}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia

${\begin{array}{rrcl}f_{n}:&\mathbb {C} &\rightarrow &\mathbb {C} \\&x&\mapsto &\displaystyle f_{n}(z)=\sum _{k=0}^{n}{\frac {1}{n!}}\cdot \left({\frac {-1}{2\cdot \sigma ^{2}}}\right)^{n}\cdot (z-\mu )^{2n}\end{array}}_{.}$

Sensitive Content Hidden
Turn off Family Mode to view

de.wikipedia.org

Visit

Normalverteilung – Wikipedia