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- Normally_distributed_and_uncorrelated_does_not_imply_independent abstract "In probability theory, two random variables being uncorrelated does not imply their independence. In some contexts, uncorrelatedness implies at least pairwise independence (as when the random variables involved have Bernoulli distributions).It is sometimes mistakenly thought that one context in which uncorrelatedness implies independence is when the random variables involved are normally distributed. However, this is incorrect if the variables are merely marginally normally distributed but not jointly normally distributed.Suppose two random variables X and Y are jointly normally distributed. That is the same as saying that the random vector (X, Y) has a multivariate normal distribution. It means that the joint probability distribution of X and Y is such that each linear combination of X and Y is normally distributed, i.e. for any two constant (i.e., non-random) scalars a and b, the random variable aX + bY is normally distributed. In that case if X and Y are uncorrelated, i.e., their covariance cov(X, Y) is zero, then they are independent. However, it is possible for two random variables X and Y to be so distributed jointly that each one alone is marginally normally distributed, and they are uncorrelated, but they are not independent; examples are given below.".
- Normally_distributed_and_uncorrelated_does_not_imply_independent thumbnail Uncorrelated_sym.png?width=300.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageID "1812223".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageLength "6280".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageOutDegree "24".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageRevisionID "683271324".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Bernoulli_distribution.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Category:Statistical_dependence.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Category:Theory_of_probability_distributions.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Continuous_function.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Correlation.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Correlation_and_dependence.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Covariance.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Cumulative_distribution_function.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Expected_value.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Independence_(probability_theory).
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Intermediate_value_theorem.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Joint_probability_distribution.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Marginal_distribution.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Multivariate_normal_distribution.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Normal_distribution.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Pairwise_independence.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Pearson_product-moment_correlation_coefficient.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Probability_theory.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Rademacher_distribution.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Random_variable.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink Statistical_independence.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink File:Uncorrelated_asym.png.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLink File:Uncorrelated_sym.png.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLinkText "Normally distributed and uncorrelated does not imply independent".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLinkText "Normally distributed and uncorrelated does not imply independent#A symmetric example".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLinkText "[proof]".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLinkText "fail".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLinkText "in general, not sufficient".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLinkText "individually normally distributed".
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageWikiLinkText "normally distributed and uncorrelated does not imply independent".
- Normally_distributed_and_uncorrelated_does_not_imply_independent hasPhotoCollection Normally_distributed_and_uncorrelated_does_not_imply_independent.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wikiPageUsesTemplate Template:Reflist.
- Normally_distributed_and_uncorrelated_does_not_imply_independent subject Category:Statistical_dependence.
- Normally_distributed_and_uncorrelated_does_not_imply_independent subject Category:Theory_of_probability_distributions.
- Normally_distributed_and_uncorrelated_does_not_imply_independent comment "In probability theory, two random variables being uncorrelated does not imply their independence. In some contexts, uncorrelatedness implies at least pairwise independence (as when the random variables involved have Bernoulli distributions).It is sometimes mistakenly thought that one context in which uncorrelatedness implies independence is when the random variables involved are normally distributed.".
- Normally_distributed_and_uncorrelated_does_not_imply_independent label "Normally distributed and uncorrelated does not imply independent".
- Normally_distributed_and_uncorrelated_does_not_imply_independent sameAs m.05yxnn.
- Normally_distributed_and_uncorrelated_does_not_imply_independent sameAs Q7051859.
- Normally_distributed_and_uncorrelated_does_not_imply_independent sameAs Q7051859.
- Normally_distributed_and_uncorrelated_does_not_imply_independent wasDerivedFrom Normally_distributed_and_uncorrelated_does_not_imply_independent?oldid=683271324.
- Normally_distributed_and_uncorrelated_does_not_imply_independent depiction Uncorrelated_sym.png.
- Normally_distributed_and_uncorrelated_does_not_imply_independent isPrimaryTopicOf Normally_distributed_and_uncorrelated_does_not_imply_independent.
