Vikipedi - Moozonian

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Yapay zekâ - Vikipedi

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Yollarda - Vikipedi

$S^{2}\sim \operatorname {Gamma} \left({\frac {n-1}{2}},{\frac {2\sigma ^{2}}{n-1}}\right).$

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Normal dağılım - Vikipedi

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Normal dağılım - Vikipedi

$Y=|X|$

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Normal dağılım - Vikipedi

$X\sim {\textrm {Levy-S}}\alpha {\textrm {S}}(2,\beta ,\sigma /{\sqrt {2}},\mu )$

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Normal dağılım - Vikipedi

$Y=X_{1}/X_{2}$

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Normal dağılım - Vikipedi

$R\sim \mathrm {Rayleigh} (\sigma ^{2})$

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Normal dağılım - Vikipedi

$-{1 \over 2}\sum x^{2}$

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Normal dağılım - Vikipedi

$X_{1},X_{2},\dots ,X_{n}\sim N(\mu /n,\sigma ^{2}\!/n)\,$

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Normal dağılım - Vikipedi

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Normal dağılım - Vikipedi

$d={\sqrt {-2\ln a}}\cdot \sin(2\pi b)$

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Normal dağılım - Vikipedi

$c={\sqrt {-2\ln a}}\cdot \cos(2\pi b)$

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Normal dağılım - Vikipedi

$E\left[x^{2k}\right]={\frac {(2k)!}{2^{k}k!}}\sigma ^{2k}.$

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Normal dağılım - Vikipedi

${\begin{aligned}\chi _{X}(t;\mu ,\sigma )&{}=M_{X}(it)=\mathrm {E} \left[\exp(itX)\right]\\&{}=\int _{-\infty }^{\infty }{\frac {1}{\sigma {\sqrt {2\pi }}}}\exp \left(-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}\right)\exp(itx)\,dx\\&{}=\exp \left(i\mu t-{\frac {\sigma ^{2}t^{2}}{2}}\right).\end{aligned}}$

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Normal dağılım - Vikipedi

${\begin{aligned}M_{X}(t)&{}=\mathrm {E} \left[\exp {(tX)}\right]\\&{}=\int _{-\infty }^{\infty }{\frac {1}{\sigma {\sqrt {2\pi }}}}\exp {\left(-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}\right)}\exp {(tx)}\,dx\\&{}=\exp {\left(\mu t+{\frac {\sigma ^{2}t^{2}}{2}}\right)}\end{aligned}}$

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Normal dağılım - Vikipedi

${\begin{aligned}{\Bigl (}1+{\frac {1}{x^{2}}}{\Bigr )}(1-\Phi (x))&=\int _{x}^{\infty }{\Bigl (}1+{\frac {1}{x^{2}}}{\Bigr )}\varphi (u)\,du\\&>\int _{x}^{\infty }{\Bigl (}1+{\frac {1}{u^{2}}}{\Bigr )}\varphi (u)\,du=-{\biggl .}{\frac {\varphi (u)}{u}}{\biggr |}_{x}^{\infty }={\frac {\varphi (x)}{x}}.\end{aligned}}$

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Normal dağılım - Vikipedi

$\Phi (x)=\Phi _{0,1}(x)={\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{x}\exp {\Bigl (}-{\frac {u^{2}}{2}}{\Bigr )}\,du,\quad x\in \mathbb {R} .$

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Normal dağılım - Vikipedi

${\begin{aligned}\Phi _{\mu ,\sigma ^{2}}(x)&{}=\int _{-\infty }^{x}\varphi _{\mu ,\sigma ^{2}}(u)\,du\\&{}={\frac {1}{\sigma {\sqrt {2\pi }}}}\int _{-\infty }^{x}\exp {\Bigl (}-{\frac {(u-\mu )^{2}}{2\sigma ^{2}}}\ {\Bigr )}\,du\\&{}=\Phi {\Bigl (}{\frac {x-\mu }{\sigma }}{\Bigr )},\quad x\in \mathbb {R} ,\end{aligned}}$

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Normal dağılım - Vikipedi

$\varphi _{\mu ,\sigma ^{2}}$

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Normal dağılım - Vikipedi