توزیع برنولی
Sign in to savediscrete probability distribution which compels the random variable to take one of two values
Key facts
- Notation
- B e r n o u l l i ( p ) {\displaystyle \mathrm {Bernoulli} (p)}
- Parameters
- 0 ≤ p ≤ 1 {\displaystyle 0\leq p\leq 1} , q = 1 − p {\displaystyle q=1-p}
- Support
- k ∈ { 0 , 1 } {\displaystyle k\in \{0,1\}}
- Pmf
- { q = 1 − p if k = 0 p if k = 1 {\displaystyle {\begin{cases}q=1-p&{\text{if }}k=0\\p&{\text{if }}k=1\end{cases}}}
- Cdf
- { 0 if k < 0 1 − p if 0 ≤ k < 1 1 if k ≥ 1 {\displaystyle {\begin{cases}0&{\text{if }}k<0\\1-p&{\text{if }}0\leq k<1\\1&{\text{if }}k\geq 1\end{cases}}}
- Mean
- p {\displaystyle p}
- Median
- 1/2\n \\end{cases}"}}'> { 0 if p < 1 / 2 [ 0 , 1 ] if p = 1 / 2 1 if p > 1 / 2 {\displaystyle {\begin{cases}0&{\text{if }}p<1/2\\\left[0,1\right]&{\text{if }}p=1/2\\1&{\text{if }}p>1/2\end{cases}}}
- Mode
- 1/2\n \\end{cases}"}}'> { 0 if p < 1 / 2 0 , 1 if p = 1 / 2 1 if p > 1 / 2 {\displaystyle {\begin{cases}0&{\text{if }}p<1/2\\0,1&{\text{if }}p=1/2\\1&{\text{if }}p>1/2\end{cases}}}
- Variance
- p ( 1 − p ) = p q {\displaystyle p(1-p)=pq}
- Mad
- 2 p ( 1 − p ) = 2 p q {\displaystyle 2p(1-p)=2pq}
- Skewness
- q − p p q {\displaystyle {\frac {q-p}{\sqrt {pq}}}}
- Excess kurtosis
- 1 − 6 p q p q {\displaystyle {\frac {1-6pq}{pq}}}
- Entropy
- − q ln q − p ln p {\displaystyle -q\ln q-p\ln p}
- Mgf
- q + p e t {\displaystyle q+pe^{t}}
- Cf
- q + p e i t {\displaystyle q+pe^{it}}
- Pgf
- q + p z {\displaystyle q+pz}
- Fisher information
- 1 p q {\displaystyle {\frac {1}{pq}}}
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Wikidata facts
- Instance of
- probability distribution
- Named after
- Jacob Bernoulli
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- Commons category
- Bernoulli distribution
- maintained by WikiProject
- WikiProject Mathematics
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