Distributione de Bernoulli

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**Bernoulli**
Funktione de probableso de mase
Funktione de akumulati distributione
Parametres	$p>0\,$ (real) $q\equiv 1-p\,$
Suporto	$k=\{0,1\}\,$
Funktione de probableso de mase (fpm)	$\begin{matrix} q & \mbox{por }k=0 \\p~~ & \mbox{por }k=1 \end{matrix}$
Funktione de akumulati distributione (fad)	$\begin{matrix} 0 & \mbox{por }k<0 \\q & \mbox{por }0<k<1\\1 & \mbox{por }k>1 \end{matrix}$
Medivalore	$p\,$
Mediane	N/A
Mode	$\textrm{max}(p,q)\,$
Variantia	$pq\,$
Nonsimetreso	$\frac{q-p}{\sqrt{pq}}$
Kurtose	$\frac{6p^2-6p+1}{p(1-p)}$
Entropie	$-q\ln(q)-p\ln(p)\,$
mgf	$q+pe^t\,$
Kar. funk.	$q+pe^{it}\,$

In probableso teorie e statistike, li Bernoulli distributione, nomat segun suisi sientiiste Jakob Bernoulli, es diskreti probableso distributione, kel have valore 1 kun probableso $p$ e valore 0 kun probableso de falio $q = 1 - p$ . Dunke si X es hasardal variable kun disi distributione, nus have:

$\Pr(X=1) =$

$1- \Pr(X=0) = p.\!$

Li probableso-mase funktione f de disi distributione es

$f(k;p) = \left\{\begin{matrix} p & \mbox {si }k=1, \\ 1-p & \mbox {si }k=0, \\ 0 & \mbox {altrim.}\end{matrix}\right.$

Li expektati valore de Bernoulli hasardal variable X es $E\left(X\right)=p$ , e lun variantia es

$\textrm{var}\left(X\right)=p\left(1-p\right).\,$

Li kurtose vada a infiniteso kun alti e basi valores de p, ma kun $p = 1 / 2$ li Bernoulli distributione have plu basi kurtose kam irgi altri probableso distributione, nomim -2.

Li Bernoulli distributione es membre del exponential familie.

[modifika] Relatet distributiones

Si $X_1,\dots,X_n$ es nondependanti, identim distributi hasardal variables, chaki havent Bernoulli distributione kun sukseso probableso p, tand
$Y = \sum_{k=1}^n X_k \sim \mathrm{Binomial}(n,p)$ (binomial distributione).

[modifika] Vida anke

Bernoulli probo
Bernoulli prosedo

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Diskreti:	Bernoulli • binomial • Boltzmann • kompositi Poisson • degenerati • gradu-nombral • Gauss-Kuzmin • geometriki • hipergeometriki • logaritmal • negativ binomial • paraboli fraktal • Poisson • Rademacher • Skellam • uniformi • Yule-Simon • zeta • Zipf • Zipf-Mandelbrot	Ewens • multinomial
Kontinui:	Beta • Beta prime • Cauchy • khi-quadrati • Delta functione de Dirac • Erlang • exponential • generalisat erore • F • fadanti • Fisher z • Fisher-Tippett • Gama • generalisat extremi valore • generalisat hiperboli • generalisat inversi Gauss • Mi-Logisti • Hotelling T-quadrati • hyperboli sekantal • hiperexponential • hipoexponential • inversi khi-quadrati • inversi Gauss • inversi gama • Kumaraswamy • Landau • Laplace • Lévy • Lévy nonsimetri alfa-stabili • logisti • log-normal • Maxwell-Boltzmann • Maxwell rapideso • normal (Gauss) • Pareto • Pearson • polar • elevati kosine • Rayleigh • relativisti Breit-Wigner • Rice • Student t • triangular • tipe-1 Gumbel • tipe-2 Gumbel • uniformi • Voigt • von Mises • Weibull • Wigner mi-sirklal	Dirichlet • Kent • matrisal normal • multivariablosi normal • von Mises-Fisher • Wigner quasi • Wishart
Diversi:	Cantor • konditional • exponential familie • infinitim divisibli • familie de lokal game • marginal • maxim entropie • fase-tipi • posterior • prior • quasi • samplanti

Kategorie: Diskreti distributiones

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Distributione de Bernoulli

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[modifika] Relatet distributiones

[modifika] Vida anke

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