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gptkbp:instanceOf
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Probability distribution
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gptkbp:application
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Genetics
Quality control
Reliability engineering
Survey sampling
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gptkbp:assumes
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Constant probability of success per trial
Fixed number of trials
Independent trials
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gptkbp:category
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gptkb:Discrete_distribution
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gptkbp:cumulativeDistributionFunction
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Sum_{i=0}^k C(n, i) p^i (1-p)^{n-i}
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gptkbp:describedYear
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1713
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gptkbp:firstDescribed
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gptkb:Ars_Conjectandi
gptkb:Jacob_Bernoulli
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gptkbp:hasSpecialCase
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Bernoulli distribution (when n=1)
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https://www.w3.org/2000/01/rdf-schema#label
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Binomial distribution
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gptkbp:kurtosis
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(1-6p(1-p))/(np(1-p))
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gptkbp:limitation
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Poisson distribution (as n→∞, p→0, np=λ)
Normal distribution (as n→∞, by Central Limit Theorem)
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gptkbp:meaning
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np
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gptkbp:mode
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floor((n+1)p)
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gptkbp:parameter
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n (number of trials)
p (probability of success)
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gptkbp:pmf
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P(X = k) = C(n, k) p^k (1-p)^{n-k}
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gptkbp:randomVariable
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Number of successes in n independent Bernoulli trials
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gptkbp:relatedTo
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gptkb:Multinomial_distribution
gptkb:Hypergeometric_distribution
gptkb:Negative_binomial_distribution
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gptkbp:skewness
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(1-2p)/sqrt(np(1-p))
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gptkbp:supports
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k = 0, 1, ..., n
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gptkbp:usedIn
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gptkb:Probability_theory
Statistics
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gptkbp:variant
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np(1-p)
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gptkbp:bfsParent
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gptkb:Beta_distribution
gptkb:Exponential_family
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gptkbp:bfsLayer
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6
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