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- | ====== Bernoulli Distribution ====== | ||
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- | In probability theory and statistics, the Bernoulli distribution, | ||
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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, | ||
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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 | ||
- | |p |Success probability|0.5 | ||
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