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bernoulli_distribution [2023/01/19 11:02]
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-====== Bernoulli Distribution ====== 
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-In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jakob Bernoulli, is a discrete probability distribution, which takes value 1 with success probability p and value 0 with failure probability q = 1 - p. So if X is a random variable with this distribution, we have: 
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-Pr(X=1)=1-Pr(X=0)=1-q=p 
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-The probability mass function f of this distribution is 
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-f(x,p) =    
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-p, if x = 1    
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-1-p, if x = 0    
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-0, otherwise 
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-The expected value of a Bernoulli random variable X is E(X)=p, and its variance is var(X)=p(1-p). 
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-The kurtosis goes to infinity for high and low values of p, but for p = 1/2 the Bernoulli distribution has a lower kurtosis than any other probability distribution, namely -5. 
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-The Bernoulli distribution is a member of the exponential family. 
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-support x = 0,…,n 
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-^Parameter^Description        ^Default value^ 
-|p        |Success probability|0.5          | 
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bernoulli_distribution.1674122566.txt.gz · Last modified: 2023/01/19 11:02 by daria