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.

[edit] 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).

[edit] Vida anke

  • Bernoulli probo
  • Bernoulli prosedo


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