The binomial distribution describes the number of "successes" in a series of Bernoulli trials. Another related distribution is the Negative Binomial, which is the distribution of the number of failures to achieve a certain number of successes.
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Parameters |
probability of success (\(p\)), number of trials (\(n\)) |
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Probability Function |
\(\left( {\begin{array}{*{20}c} n \\ k \\ \end{array}} \right)p^k (1 - p)^{n - k}\) |
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Support |
Number of successes (\(k\)) in {0,...,\(n\)} |
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Mean |
\(np\) |
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Variance |
\(np(1-p)\) |
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Probability Functions |
%BINOMIALK(k,n,p) is the probability of exactly \(k\) successes given parameters \(n\) and \(p\).
%BINOMIALCDF(k,n,p) is the cumulative probability of no more than \(k\) successes given parameters \(n\) and \(p\). |
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