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Chebyshev's inequality with one-tailed and unimodal versions, putting statistical limits on the dispersion of probability distributions.
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Discussion and proof Chebyshev's inequality in statistics and
and a one-tailed version. By Henry Bottomley
Chebyshev's inequality states that P[|X-E(X)|>=t] <= Var(X)/t 2 which is equivalent to for k>0 P[|X-E(X)|>=k.sd(X)] <= 1/k 2 A one-tailed version of Chebyshev's inequality is that for t>0 P[X-E(X)>=t] <= 1/(1 + t 2 /Var(X)) i.e. P[X-E(X)>=t] <= Var(X)/(Var(X) + t
Chebyshev's inequality states that P[|X-E(X)|>=t] <= Var(X)/t 2 which is equivalent to for k>0 P[|X-E(X)|>=k.sd(X)] <= 1/k 2 A one-tailed version of Chebyshev's inequality is that for t>0 P[X-E(X)>=t] <= 1/(1 + t 2 /Var(X)) i.e. P[X-E(X)>=t] <= Var(X)/(Var(X) + t
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Covers mean, mode, median, standard deviation, area approximation, charts and testing for normality.
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Primer in Statistics includes basic statistical topics; Advanced Statistics includes regression analysis, ANOVA, hypothesis testing, and other advanced topics. Free Introduction to Statistics module and free Excel Primer.
of statistics have been explained in a beautiful manner which makes them easy to understand. " "The format of this course is excellent and ensures that each principle has been fully understood before moving on to the next." in Statistics and Advanced Statistics are aimed at professionals
of statistics have been explained in a beautiful manner which makes them easy to understand. " "The format of this course is excellent and ensures that each principle has been fully understood before moving on to the next." in Statistics and Advanced Statistics are aimed at professionals
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This resource for teaching statistics includes java simulations, case studies, an online text, and an analysis lab.
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Web based materials for teaching statistics. Includes simulations, demonstrations, case studies, and an online statistics textbook.
Rice Virtual Lab in Statistics support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not
Rice Virtual Lab in Statistics support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not
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